Method for setting cyclic shift considering frequency offset

ABSTRACT

A method for transmitting a random access preamble to a base station includes generating the random access preamble from a Zadoff-Chu (ZC) sequence having a length N, wherein the random access preamble is generated by considering a cyclic shift of the ZC sequence; and transmitting the random access preamble to the base station, wherein the cyclic shift is given by using a variable M corresponding to a Doppler shift of one subcarrier spacing, and wherein parameters associated with defining the cyclic shift are differently defined based on whether the variable M is less than ⅓ of the length N.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of Korean Patent Application No.10-2007-0011772, filed on Feb. 5, 2007 and Korean Patent Application No.10-2007-00102563, filed on Oct. 11, 2007, which are hereby incorporatedby reference as if fully set forth herein.

This application also claims the benefit of U.S. Provisional ApplicationSer. No. 60/883,754, filed on Jan. 5, 2007, U.S. Provisional ApplicationSer. No. 60/884,398, filed on Jan. 10, 2007, U.S. ProvisionalApplication Ser. No. 60/915,096, filed on Apr. 30, 2007 and U.S.Provisional Application Ser. No. 60/941,562, filed on Jun. 1, 2007, thecontents of which are hereby incorporated by reference herein in theirentirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a sequence of a wireless communicationsystem, and more particularly to a method for establishing a cyclicshift in consideration of characteristics of a CAZAC sequence in orderto solve the problem of a frequency offset.

2. Discussion of the Related Art

A Constant Amplitude Zero Auto-Correlation (CAZAC) sequence is arepresentative one of various sequences which have been intensivelydiscussed in the 3GPP LTE.

Channels generally extract a variety of identifiers (IDs) or informationusing the CAZAC sequence, for example, synchronization channels (e.g., aprimary-SCH, a secondary-SCH, and a BCH) for downlink synchronization,other synchronization channels (e.g., a RACH) for uplinksynchronization, and pilot channels (e.g., a data pilot, and a channelquality pilot). Also, the above-mentioned CAZAC sequence has been usedto perform the scrambling.

Two kinds of methods have been used for the CAZAC sequence, i.e., afirst method for changing a root index to another, and employing thechanged root index, and a second method for performing a cyclic shift(CS) on a single root sequence, and employing the CS-result.

If a current root index is changed to a new root index, a lowcross-correlation occurs between the current root index and the new rootindex, however, there is no limitation in designing sequence usages.

In the case of the cyclic shift, zero cross-correlation exists betweenthe current root index and the new root index, so that the two rootindexes are used when each of the root indexes require a high rejectionratio. Specifically, when time-frequency resources are shared in thesame cell and data/control signals are transmitted, the above-mentionedtwo root indexes are adapted to discriminate among different signals orUEs.

A representative example of CAZAC sequences is a Zadoff-Chu (ZC)sequence, and the Zadoff-Chu sequence can be defined by the followingequation 1:

$\begin{matrix}{\begin{matrix}{{x_{u}(n)} = {\exp \left( \frac{j\; u\; \pi \; {n\left( {n + 1} \right)}}{N_{ZC}} \right)}} & {{for}\mspace{14mu} {odd}\mspace{14mu} {Nzc}}\end{matrix}\begin{matrix}{{x_{u}(n)} = {\exp \left( \frac{j\; u\; \pi \; n^{2}}{N_{ZC}} \right)}} & {{for}\mspace{14mu} {odd}\mspace{14mu} {Nzc}}\end{matrix}} & \left\lbrack {{Equation}\mspace{14mu} 1} \right\rbrack\end{matrix}$

where “n” is indicative of a sampling index, “Nzc” is indicative of thelength of the ZC sequence, and “u” is indicative of the root index ofthe ZC sequence.

However, if the offset occurs in a frequency domain in the same manneras in the case where the CAZAC sequence is transmitted using the OFDMscheme, a performance or false alarm or throughput may be excessivelydeteriorated.

Specifically, if the cyclic shift (CS) is applied to the CAZAC sequence,the frequency offset or the timing offset excessively occurs, so that itis difficult to discriminate between sequences.

SUMMARY OF THE INVENTION

Accordingly, the present invention is directed to a method forestablishing a cyclic shift (CS) considering a frequency offset thatsubstantially obviates one or more problems due to limitations anddisadvantages of the related art.

An object of the present invention is to provide a method forestablishing a cyclic shift (CS) to provide against a frequency offset,so that it can easily prevent a sequence (e.g., a CAZAC sequence) frombeing deteriorated under the condition that the frequency offset occurs.

Additional advantages, objects, and features of the invention will beset forth in part in the description which follows and in part willbecome apparent to those having ordinary skill in the art uponexamination of the following or may be learned from practice of theinvention. The objectives and other advantages of the invention may berealized and attained by the structure particularly pointed out in thewritten description and claims hereof as well as the appended drawings.

To achieve these objects and other advantages and in accordance with thepurpose of the invention, as embodied and broadly described herein, amethod for setting cyclic shift to be applied to a given sequenceagainst an effect of a high Doppler frequency higher than apredetermined value is provided. According to the method, the methodcomprises: acquiring a first variable (d_(u)) of cyclic shiftcorresponding to a Doppler shift of one subcarrier spacing by using anroot index (u) of the given sequence; acquiring secondary variablescomprising a number of group (G) comprised in the given sequence, alength of the each group (S) and a number of cyclic shift per the group(P) using the first variable (d_(u)); and establishing the cyclic shiftto be applied to the given sequence according to the secondaryvariables.

Preferably, the secondary variables further comprise a number ofadditional cyclic shifts which are applicable to the given sequence notbased on the group (R).

Preferably, the given sequence is a Zadoff-Chu (ZC) sequence, and thefirst variable is acquired by a equation of,

$d_{u} = \left\{ \begin{matrix}{{u^{- 1}\mspace{14mu} {mod}\mspace{14mu} N_{ZC}},{0 \leq \left( {u^{- 1}\mspace{14mu} {mod}\mspace{14mu} N_{ZC}} \right) < {N_{ZC}/2}}} \\{{N_{ZX} - \left( {u^{- 1}\mspace{14mu} {mod}\mspace{14mu} N_{ZC}} \right)},{{N_{ZC}/2} \leq \left( {u^{- 1}\mspace{14mu} {mod}\mspace{14mu} N_{ZC}} \right) < N_{ZC}}}\end{matrix} \right.$

wherein “u” indicates the root index of the ZC sequence and “N_(ZC)”corresponds to a length of the ZC sequence.

And, in this case, the secondary variables are differently acquiredaccording to a range of the first variable (d_(u)), and the range of thefirst variable is divided by a criteria corresponding to ⅓ of the givensequence length (Nzc/3).

And, if the range of the first variable (d,) is Ncs≦d_(u)≦(Nzc/3), thesecondary variables may be acquired by equations of,

P=└d _(u) /N _(CS)┘

S=2·d _(u) +P·N _(CS)

G=└N _(ZC) /S┘

R=max(└(N _(ZC)−2·d_(u) −G·S)/N _(CS)┘, 0)

wherein “N_(CS)” is a predetermined cyclic shift parameter, “P”corresponds to the number of cyclic shift per the group, “S” correspondsto the length of the each group, “G” corresponds to the number of groupand “R” corresponds to the number of additional cyclic shifts.

On the other hand, if the range of the first variable (d_(u)) is(Nzc/3)≦d≦(Nzc−Ncs)/2, the secondary variables may be acquired byequations of,

P=└(N _(ZC)−2·D _(u))/N _(CS)┘

S=N _(ZC)−2·d _(u) +P·N _(CS)

G=└d _(u) /S┘

R=min(max(└(d _(u) −G·S)/N _(CS)┘, 0), P)

wherein “N_(CS)” is a predetermined cyclic shift parameter, “P”corresponds to the number of cyclic shift per the group, “S” correspondsto the length of the each group, “G” corresponds to the number of groupand “R” corresponds to the number of additional cyclic shifts.

And, preferable, said establishing the cyclic shift (C_(v)) is performedas a equation of,

C _(v) =S·└/P┘+(v mod P)·N _(CS) , v=0, 1, . . . , (P·G+R−1).

And, the given sequence may be for generating a random access preamble.

In another aspect of the present invention, there is provided a methodfor setting cyclic shift to be applied to a given sequence, the methodcomprising: determining whether the cyclic shift is to be establishedaccording to a restricted sets restricted due to a Doppler shift; andestablishing the cyclic shift to be applied to the given sequenceconsidering a cyclic shift corresponding to a Doppler shift of onesubcarrier spacing, when the cyclic shift is determined to beestablished according to the restricted sets.

Preferably, when the cyclic shift is determined to be establishedaccording to the restricted sets, said establishing the cyclic shift tobe applied to the given sequence comprises: acquiring a first variable(d_(u)) indicating the cyclic shift corresponding to the Doppler shiftof one subcarrier spacing by using an root index (u) of the givensequence; acquiring secondary variables comprising a number of group (G)comprised in the given sequence, a length of the each group (S), anumber of cyclic shift per the group (P) using the first variable(d_(u)) and a number of additional cyclic shifts which is applicable tothe given sequence not based on the group (R), and establishing thecyclic shift to be applied to the given sequence according to thesecondary variables.

Preferably, the given sequence is a Zadoff-Chu (ZC) sequence, and

the first variable is acquired by a equation of,

$d_{u} = \left\{ \begin{matrix}{{u^{- 1}\mspace{14mu} {mod}\mspace{14mu} N_{ZC}},{0 \leq \left( {u^{- 1}\mspace{14mu} {mod}\mspace{14mu} N_{ZC}} \right) < {N_{ZC}/2}}} \\{{N_{ZC} - \left( {u^{- 1}\mspace{14mu} {mod}\mspace{14mu} N_{ZC}} \right)},{{N_{ZC}/2} \leq \left( {u^{- 1}\mspace{14mu} {mod}\mspace{14mu} N_{ZC}} \right) < N_{ZC}}}\end{matrix} \right.$

wherein “u” indicates the root index of the ZC sequence and “N_(ZC)”corresponds to a length of the ZC sequence.

And, the secondary variables may be differently acquired according to arange of the first variable (d_(u)), and the range of the first variableis divided by a criteria corresponding to ⅓ of the given sequence length(Nzc/3).

In this case, if the range of the first variable (d_(u)) isNcs≦d_(u)<(Nzc/3), the secondary variables are acquired by equations of,

P=└d _(u) /N _(CS)┘

S=2·d _(u) +P·N _(CS)

G=└N _(ZC) /S┘

R=max(└(N _(ZC)−2·d _(u) −G·S)/N _(CS)┘, 0)

wherein “N_(CS)” is a predetermined cyclic shift parameter, “P”corresponds to the number of cyclic shift per the group, “S” correspondsto the length of the each group, “G” corresponds to the number of groupand “R” corresponds to the number of additional cyclic shifts.

On the other hand, if the range of the first variable (d_(u)) is(Nzc/3)≦d_(u)≦(Nzc−Ncs)/2, the secondary variables are acquired byequations of,

P=└(N _(ZC)−2·d _(u))/N _(CS)┘

S=N _(ZC)−2·d _(u) +P·N _(CS)

G=└d _(u) /S┘

R=min(max(└(d _(u) −G·S)/N _(CS)┘, 0), P)

wherein “N_(CS)” is a predetermined cyclic shift parameter, “P”corresponds to the number of cyclic shift per the group, “S” correspondsto the length of the each group, “G” corresponds to the number of groupand “R” corresponds to the number of additional cyclic shifts.

And, preferably, the cyclic shift (C_(v)) is performed as followingequation,

$C_{v} = \left\{ {\begin{matrix}{{v \cdot N_{CS}},{v = 0},1,K,\left( {\left\lfloor {N_{ZC}/N_{CS}} \right\rfloor - 1} \right),} & {{for}\mspace{14mu} {unrestricted}\mspace{14mu} {sets}} \\{{{S \cdot \left\lfloor {v/P} \right\rfloor} + {\left( {v\mspace{14mu} {mod}\mspace{14mu} P} \right) \cdot N_{CS}}},{v = 0},1,K,\left( {{P \cdot G} + R - 1} \right),} & {{for}\mspace{14mu} {restricted}\mspace{14mu} {sets}}\end{matrix}.} \right.$

And, the given sequence may be for generating a random access preamble.

In another aspect of the present invention, there is provided a methodfor setting cyclic shift to be applied to a given sequence, the methodcomprising: (a) acquiring a variable of d_(u) by a equation of,

$d_{u} = \left\{ \begin{matrix}{{u^{- 1}\mspace{14mu} {mod}\mspace{14mu} N_{ZC}},{0 \leq \left( {u^{- 1}\mspace{14mu} {mod}\mspace{14mu} N_{ZC}} \right) < {N_{ZC}/2}}} \\{{N_{ZC} - \left( {u^{- 1}\mspace{14mu} {mod}\mspace{14mu} N_{ZC}} \right)},{{N_{ZC}/2} \leq \left( {u^{- 1}\mspace{14mu} {mod}\mspace{14mu} N_{ZC}} \right) < N_{ZC}}}\end{matrix} \right.$

wherein “u” indicates an root index of the given sequence and “N_(ZC)”corresponds to a length of the given sequence; (b) acquiring variablesof G, S, P and R by equations of,

P=└d _(u) /N _(CS)┘

S=2·d _(u) +P·N _(CS)

G=└N _(ZC) /S┘

R=max(└(N_(ZC)−2·d_(u)−G·S)/N_(CS)┘, 0) when a range of the firstvariable (d_(u)) is Ncs≦d_(u)<(Nzc/3), and acquiring variables of G, S,P and R by equations of,

P=└(N _(ZC)−2·d _(u))/N _(CS)┘

S=N _(ZC)−2·d _(u) +P·N _(CS)

G=└d _(u) /S┘

R=min(max(└(d_(u)−G·S)/N_(CS)┘, 0), P) when the range of the firstvariable (d_(u)) is (Nzc/3)≦d_(u)≦(Nzc−Ncs)/2,

wherein “N_(CS)” is a predetermined cyclic shift parameter; (c)establishing the cyclic shift (C_(v)) by equation of,

$C_{v} = \left\{ \begin{matrix}{{v \cdot N_{CS}},{v = 0},1,K,\left( {\left\lfloor {N_{ZC}/N_{CS}} \right\rfloor - 1} \right),} & {{for}\mspace{14mu} {unrestricted}\mspace{14mu} {sets}} \\{{{S \cdot \left\lfloor {v/P} \right\rfloor} + {\left( {v\mspace{14mu} {mod}\mspace{14mu} P} \right) \cdot N_{CS}}},{v = 0},1,K,\left( {{P \cdot G} + R - 1} \right),} & {{for}\mspace{14mu} {restricted}\mspace{14mu} {sets}}\end{matrix} \right.$

wherein the restricted sets are a cyclic shift sets restricted due to aDoppler shift, and the unrestricted sets are a cyclic shift sets notrestricted due to the Doppler shift.

In another aspect of the present invention, there is provided a methodfor transmitting a random access preamble using cyclic shift, the methodcomprising: acquiring a root index (u) of a sequence for the randomaccess preamble from system information; establishing the cyclic shiftto be applied to the sequence, in said establishing, when the cyclicshift is determined to be established according to the restricted setsrestricted due to a Doppler shift, the cyclic shift to be applied to thesequence is established by considering a cyclic shift corresponding to aDoppler shift of one subcarrier spacing; generating the sequenceaccording to the root index (u) with the established cyclic shift; andtransmitting the sequence with the cyclic shift as the random accesspreamble.

Preferably, when the cyclic shift is determined to be establishedaccording to the restricted sets, said establishing the cyclic shift tobe applied to the sequence comprises: acquiring a first variable (d_(u))indicating the cyclic shift corresponding to the Doppler shift of onesubcarrier spacing by using the root index (u) of the given sequence;acquiring secondary variables comprising a number of group (G) comprisedin the sequence, a length of the each group (S), a number of cyclicshift per the group (P) using the first variable (d_(u)) and a number ofadditional cyclic shifts which is applicable to the sequence not basedon the group (R), and establishing the cyclic shift to be applied to thesequence according to the secondary variables.

Preferably, wherein the given sequence is a Zadoff-Chu (ZC) sequence,and the first variable is acquired by a equation of,

$d_{u} = \left\{ \begin{matrix}{{u^{- 1}\mspace{14mu} {mod}\mspace{14mu} N_{ZC}},{0 \leq \left( {u^{- 1}\mspace{14mu} {mod}\mspace{14mu} N_{ZC}} \right) < {N_{ZC}/2}}} \\{{N_{ZC} - \left( {u^{- 1}\mspace{14mu} {mod}\mspace{14mu} N_{ZC}} \right)},{{N_{ZC}/2} \leq \left( {u^{- 1}\mspace{14mu} {mod}\mspace{14mu} N_{ZC}} \right) < N_{ZC}}}\end{matrix} \right.$

wherein “u” indicates the root index of the ZC sequence and “N_(ZC)”corresponds to a length of the ZC sequence.

Preferably, wherein the secondary variables are differently acquiredaccording to a range of the first variable (d_(u)), and the range of thefirst variable is divided by a criteria corresponding to ⅓ of the givensequence length (Nzc/3).

More specifically, if the range of the first variable (d_(u)) isNcs≦d_(u)<(Nzc/3), the secondary variables may be acquired by equationsof,

P=└d _(u) /N _(CS)┘

S=2·d _(u) +P·N _(CS)

G=└N _(ZC) /S┘

R=max(└(N _(ZC)−2·d _(u) −G·S)/N _(CS)┘, 0)

wherein “N_(CS)” is a predetermined cyclic shift parameter, “P”corresponds to the number of cyclic shift per the group, “S” correspondsto the length of the each group, “G” corresponds to the number of groupand “R” corresponds to the number of additional cyclic shifts.

On the other hand, if the range of the first variable (d_(u)) is(Nzc/3)≦d_(u)≦(Nzc−Ncs)/2, the secondary variables are acquired byequations of,

P=└(N _(ZC)−2·d _(u))/N _(CS)┘

S=N _(ZC)−2·d _(u) +P·N _(CS)

G=└d _(u) /S┘

R=min(max(└(d _(u) −G·S)/N_(CS)┘, 0), P)

wherein “N_(CS)” is a predetermined cyclic shift parameter, “P”corresponds to the number of cyclic shift per the group, “S” correspondsto the length of the each group, “G” corresponds to the number of groupand “R” corresponds to the number of additional cyclic shifts.

And, preferably, wherein the cyclic shift (C_(v)) is performed asfollowing equation,

$C_{v} = \left\{ {\begin{matrix}{{v \cdot N_{CS}},{v = 0},1,K,\left( {\left\lfloor {N_{ZC}/N_{CS}} \right\rfloor - 1} \right),} & {{for}\mspace{14mu} {unrestricted}\mspace{14mu} {sets}} \\{{{S \cdot \left\lfloor {v/P} \right\rfloor} + {\left( {v\mspace{14mu} {mod}\mspace{14mu} P} \right) \cdot N_{CS}}},{v = 0},1,K,\left( {{P \cdot G} + R - 1} \right),} & {{for}\mspace{14mu} {restricted}\mspace{14mu} {sets}}\end{matrix}.} \right.$

It is to be understood that both the foregoing general description andthe following detailed description of the present invention areexemplary and explanatory and are intended to provide furtherexplanation of the invention as claimed.

The present invention can easily establish a cyclic shift (CS) intervalat a specific location having no overlapping by considering a channelresponse of a reception (Rx) sequence and an alias location of thisreception (Rx) sequence, although a reception (Rx) signal is shifted bya frequency offset irrespective of categories of a domain generating asequence, so that it can greatly reduce the number of the detectionerrors and the false alarm rate.

And, if a sequence of the cyclic shift (CS) is allocated to a cellhaving a frequency offset of more than a predetermined level, thepresent invention can minimize the influence of a frequency offset on ahigh-mobility cell.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are included to provide a furtherunderstanding of the invention, illustrate embodiments of the inventionand together with the description serve to explain the principle of theinvention.

In the drawings:

FIG. 1 is a conceptual diagram illustrating the influence of a frequencyoffset caused by a pulse shaping in a frequency domain when a sequenceis mapped to a sub-carrier according to the present invention;

FIG. 2 is a conceptual diagram illustrating different frequency offsetsituations existing in a plurality of cells according to the presentinvention;

FIG. 3 is a conceptual diagram illustrating a sequence allocation methodwhen a sequence is a CAZAC sequence according to the present invention;

FIG. 4 is a conceptual diagram illustrating aliases which occur in atime-domain channel response of a reception sequence due to thefrequency offset according to the present invention;

FIG. 5 is a conceptual diagram illustrating a method for establishing anew cyclic shift (CS)—applying unit by adding an additional margin to anold CS-applying unit according to the present invention;

FIGS. 6 and 7 are conceptual diagrams illustrating application examplesof the additional margin of FIG. 5 under the condition that a sequenceindex is low according to the present invention;

FIGS. 8 and 9 are conceptual diagram illustrating exemplary additionalmargins of FIG. 5 under the condition that a sequence index is highaccording to the present invention;

FIG. 10 shows an example of a single group composed of Pcyclic-shift-sets according to the present invention;

FIG. 11 is a conceptual diagram illustrating a method for establishing acyclic shift (CS)—applying group and the CS-applying interval of eachgroup according to the present invention;

FIG. 12 shows locations at which pulses occur by an interference whenthe CAZAC index is contained in the interval of N/3˜N/2 according to thepresent invention;

FIG. 13 is a flow chart illustrating a restricted cyclic shift setaccording to one embodiment of the present invention;

FIG. 14 is a conceptual diagram illustrating a method for establishing avariable (d,) of a cyclic shift corresponding to the Doppler shiftassociated with the 1 sub-carrier spacing when the restricted cyclicshift set is established according to the present invention;

FIG. 15 is a conceptual diagram illustrating a specific case in whichthe variable (d,) is less than a basic unit N_(CS) to which the cyclicshift (CS) is applied according to the present invention;

FIG. 16 is a conceptual diagram illustrating a method for calculating avariable establishing the cyclic shift within the interval ofN_(CS)≦d_(u)<(N_(ZC)/3) according to the present invention;

FIG. 17 is a conceptual diagram illustrating a method for calculating avariable establishing the cyclic shift within the interval of(N_(ZC)/3)≦d_(u)<(N_(ZC)−N_(CS))/2 according to the present invention;

FIGS. 18 and 19 are conceptual diagrams illustrating a method forreducing the number of ZCZ preamble sequences due to an alias responsein the case of Nzc=839, Ncs=100, and d_(u)=155 according to the presentinvention;

FIG. 20 is a conceptual diagram illustrating the increasing ratio of anavailable restricted cyclic shift after the restriction of a startlocation of the cyclic shift is removed in the case of Nzc=839 accordingto the present invention;

FIG. 21 is a conceptual diagram illustrating an exemplary cyclic shiftin the case of Nzc=839, Ncs=40, and d_(u)=150 according to oneembodiment of the present invention;

FIG. 22 is a conceptual diagram illustrating an exemplary cyclic shiftin the case of Nzc=839, Ncs=40, and d_(u)=399 according to oneembodiment of the present invention;

FIG. 23 is a conceptual diagram illustrating an exemplary cyclic shiftin the case of Nzc=839, Ncs=40, and d_(u)=150 according to anotherembodiment of the present invention; and

FIG. 24 is a conceptual diagram illustrating an exemplary cyclic shiftin the case of Nzc=839, Ncs=40, and d_(u)=399 according to anotherembodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Reference will now be made in detail to the preferred embodiments of thepresent invention, examples of which are illustrated in the accompanyingdrawings. Wherever possible, the same reference numbers will be usedthroughout the drawings to refer to the same or like parts.

Prior to describing the present invention, it should be noted that mostterms disclosed in the present invention correspond to general termswell known in the art, but some terms have been selected by theapplicant as necessary and will hereinafter be disclosed in thefollowing description of the present invention. Therefore, it ispreferable that the terms defined by the applicant be understood on thebasis of their meanings in the present invention.

For the convenience of description and better understanding of thepresent invention, general structures and devices well known in the artwill be omitted or be denoted by a block diagram or a flow chart.Wherever possible, the same reference numbers will be used throughoutthe drawings to refer to the same or like parts.

The present invention provides a cyclic shift (CS) setup method toprovide against the frequency offset, so that it can easily prevent asequence (i.e., CAZAC sequence) performance from being deteriorated. Forthis purpose, the present invention will disclose the method forapplying the cyclic shift to the CAZAC sequence, and the influence ofthe frequency offset of the CAZAC sequence.

The cyclic shift may be applied to the CAZAC sequence according to twoschemes, i.e., a first scheme for performing the cyclic shift on thesequence, and a method for multiplying an exponential function of otherareas by a time- or frequency-domain sequence, and performing the cyclicshift on the multiplied result.

The cyclic shift “d” is applied to the frequency index “k” in thefrequency domain. If the sequence index of M and the N-length sequenceis represented by c(k; d, M, N), a method for performing the cyclicshift on the sequence can be represented by the following equation 2:

c(k; d, M, N)=c(mod(k−d, N); M, N)   [Equation 2]

Where “d” is indicative of an amount of the cyclic shift, and “mod” isindicative of a modular operator.

A method for applying the cyclic shift by multiplying an exponentialfunction by the sequence can be represented by the following equation 3:

$\begin{matrix}\begin{matrix}{{c\left( {{k;d},M,N} \right)} = {f\left( {{{{mod}\left( {{k - d},N} \right)};M},N} \right)}} \\{= {{\exp \left( \frac{{j2\pi}\; {dk}}{N} \right)}{{FFT}\left( {c\left( {{k;d},M,N} \right)} \right)}}}\end{matrix} & \left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack\end{matrix}$

In the meantime, although each of the above Equations 2 and 3 shows anexemplary cyclic shift applied in the frequency domain, the cyclic shiftmay be applied in the time-domain sequence sampling index “n” in thetime domain. In this case, an application example of the cyclic shiftcan be represented by the following equation 4:

x _(u,v)(n)=x _(u)((n+C _(v))mod N _(ZC))   [Equation 4]

where “C_(v)” is indicative of the degree of the cyclic shift, “n” isindicative of a sampling index, “N_(zc)” is indicative of theZC-sequence length, and “u” is indicative of an root index of the ZCsequence.

The CAZAC sequences can be distinguished from each other under thecondition that different root indexes are used, however, it should benoted that a difference in cross-correlation occurs among the CAZACsequences.

However, in the case of at least two CAZAC sequences associated with thecyclic shift, the cross-correlation value between the CAZAC sequences iszero, so that the above-mentioned CAZAC sequences are used when a highrejection ratio is required for the two CAZAC sequences.

Specifically, the CAZAC sequence associated with the cyclic shift sharethe time-frequency resources within the same cell, so that they can beused to discriminate among different signals/UEs during the transmissionof data/control signals.

However, if the frequency offset occurs in the frequency domain in thesame manner as in the case in which the CAZAC sequence is transmittedusing the OFDM scheme, the present invention may encounter the excessivedeterioration of a performance and false alarm rate.

The following description will disclose an example in which the sequenceis transmitted in the frequency domain, and another example in which thesequence is transmitted using the OFDM scheme.

FIG. 1 is a conceptual diagram illustrating the influence of a frequencyoffset caused by a pulse shaping in a frequency domain when a sequenceis mapped to a sub-carrier according to the present invention.

As shown in FIG. 1, each of sequence samples is mapped to thesub-carrier. If a reception end performs the signal sampling due to thefrequency offset as denoted by the location of “Interference”, signalsof neighboring sub-carriers are mixed within a single sample. In otherwords, if the pulse-shaping function is p(x), the response of anarbitrary sub-carrier can be represented by the following equation 5:

$\begin{matrix}{{r\left( {k,f_{off}} \right)} = {\sum\limits_{n = 0}^{N - 1}{{p\left( {{kw}_{0} - {nw}_{0} + f_{off}} \right)}{c(n)}}}} & \left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack\end{matrix}$

where “r(k, f_(off))” is indicative of a reception (Rx)-frequencyresponse at the k-th sub-carrier location if the frequency offset isf_(off), “c(n)” is indicative of a CAZAC sequence mapped to thesub-carrier by the user equipment (UE), “p(f)” is indicative of apulse-shaping function in a frequency domain, and w_(o) is indicative ofa sub-carrier spacing.

In the case of f_(off)=0, the above Equation 5 outputs only the valuec(k). Otherwise, in the case of f_(off)≠0, the signal of the neighboringsub-carrier may enter the reception end, so that there arises aperformance deterioration. Due to the performance deterioration causedby the frequency offset, the probability of encountering the detectionerror in the reception end increases, and the false alarm rate and/ormiss-detection may unavoidably increase in the reception end.

Specifically, provided that the cyclic shift is applied in the timedomain and the CAZAC sequence is transmitted within the frequencydomain, one may not discriminate among various sequences. And, theabove-mentioned problem may occur in a situation, even when the CAZACsequence is transmitted within the time domain as a form of the timingoffset.

In other words, if the frequency offset or the timing offset occurs,methods for employing the cyclic shift must unavoidably experience theperformance deterioration. Also, the influence of the frequency offsetis equally applied to a specific case in which the cyclic shift isapplied in the time domain as denoted by Equation 4.

Therefore, there must be newly developed a technology for preventing aperformance of the sequence (i.e., CAZAC sequence) from beingdeteriorated under the condition that the frequency offset occurs.

Specifically, in the case of applying the cyclic shift to the CAZACsequence, the frequency offset or the timing offset excessively occurs,so that the present invention has difficulty in discriminating amongsequences when the frequency- or timing-offset occupies at least thehalf of a single sub-carrier spacing.

However, the degree of the frequency offset and the degree of theDoppler shift may be different in individual cells of a cellular mobilecommunication system.

Therefore, according to one embodiment, the present invention providesdifferent cyclic shift (CS) setup methods according to the degree offrequency offsets of the individual cells, and a detailed descriptionthereof will hereinafter be described.

FIG. 2 is a conceptual diagram illustrating different frequency offsetsituations existing in a plurality of cells according to the presentinvention.

Referring to FIG. 2, the present invention may determine that a specificcell having many high-mobility UEs in a cellular mobile communicationsystem including many cells has a high frequency offset. There is everyprobability that a UE contained in a cell including residentialdistricts may be a low-speed UE, so that the frequency offset within thecell may be low.

In more detail, FIG. 2 shows cells A and B adjacent to a high-speedrailway, and the cell C distant from the high-speed railway.

In the case of the cells A and B adjacent to the high-speed railway,there is every probability that a plurality of high-speed UEs arecontained in a corresponding cell, so that the present invention has anadvantage in that a sequence which is very resistant to the frequencyoffset may be allocated.

For example, in the case of the cell C adjacent to the residentialdistrict distant from the high-speed railway, the probability ofincluding the high-speed UE in a corresponding cell is relatively low,so that there is no need to allocate only the sequence which is veryresistant to the frequency offset.

In the case of the available sequence (e.g., the CAZAC sequence), firstsequences caused by the root indexes of the individual sequences andsecond sequences caused by the cyclic shift applied to the firstsequences may have different frequency offset characteristics.

Therefore, the present invention establishes the restricted case and theunrestricted case, and provides the cyclic shift setup methods for theindividual cases.

The restricted case indicates that the influence of the Doppler shift ishigher than a predetermined threshold value so that an unexpectedlimitation occurs in the process for establishing a cyclic shift(CS)—applying interval.

The unrestricted case indicates that the influence of the Doppler shiftis equal to or less than the predetermined threshold value, so thatthere is no limitation in the process for establishing the CS-applyinginterval.

The method for establishing the cyclic shift will hereinafter bedescribed in detail.

FIG. 3 is a conceptual diagram illustrating a sequence allocation methodwhen a sequence is a CAZAC sequence according to the present invention.

The CAZAC sequence may include a root sequence of each root CAZACsequence and a Zero Correlation Zone (ZCZ) sequence to which differentcyclic shifts (also called circular shifts) are applied.

In more detail, FIG. 3 shows the root sequence for each root index in Ntroot indexes, and the ZCZ-sequence set to which L cyclic shifts areapplied to each root sequence.

In this case, the ZCZ is indicative of a cyclic shift—applying intervalto which the cyclic shift (CS) is applied, so that the Node-B is able todiscriminate among RACH signals.

In the meantime, if the CAZAC sequence is used when the frequency offsetexists, the present invention may have difficulty in discriminatingamong ZCZ sequences by the frequency offset. Therefore, the presentinvention may determine that the ZCZ sequence is not used in apredetermined cell having a frequency offset of more than apredetermined level.

In this way, the threshold value used to decide the degree of thefrequency offset of each cell may be properly decided according to thenumber of available sequences of a corresponding system and thefrequency offset degree of each cell.

If it is determined that the cell has the frequency offset of more thanthe predetermined level, the probability of containing the high-speed UEin this cell is very high as shown in the cell A or B.

However, if it is determined that the ZCZ sequence is not used in thecell having the frequency offset of more than the predetermined level,there may be only Nt indexes based on the CAZAC indexes, so that thenumber of available sequences becomes lower.

If a sequence re-use coefficient becomes lower, one must allocatesequences according to the cell planning. However, this allocation basedon the cell planning may unexpectedly increase the complexity in theprocess for allocating the sequences to individual cells, so thatanother solution may be additionally required on the condition that thenumber of available sequences encounters the problem.

Furthermore, in case of using only Nt sequences and not using the ZCZsequence, there may be a problem in estimating round trip delay orone-way trip delay while the performance of detecting sequence isenhanced. That is, there may be a problem of distinguishing the positionof correlation peak varying due to the round trip delay or one-way tripdelay, and a position of correlation peak varying due to the frequencyoffset. So, another solution may be additionally required against thisproblem.

In the meantime, the above-mentioned problem having difficulty indiscriminating among ZCZ sequences due to the frequency offset becomesintensified on the condition that the CAZAC index is very high or is notvery low.

In more detail, provided that “k” is indicative of a frequency-domainindex, “N” is indicative of the CAZAC-sequence length, “M” is indicativeof a CAZAC sequence, and a transmission (Tx) signal is indicative of“c(k,N,M)”, a reception (Rx) signal can be represented by the followingequation 6:

$\begin{matrix}{{R\left( {k,N,M} \right)} = {{c\left( {K,N,M} \right)} \cdot {\exp \left( {{- \frac{2\pi \; {M \cdot d}}{N}} \cdot k} \right)}}} & \left\lbrack {{Equation}\mspace{14mu} 6} \right\rbrack\end{matrix}$

where “d” is indicative of the amount of a frequency-domain delay causedby the frequency offset.

As can be seen from Equation 6, if the CAZAC index “M” has a very lowvalue, or if the CAZAC index “M” has the highest value from among atotal of Nt sequence indexes, the influence of the exponential functioncaused by the frequency offset is gradually reduced, so that theinfluence of the frequency offset in the Rx signal is gradually reduced.

If the CAZAC sequence is allocated to the cell having the frequencyoffset of more than the predetermined level, the present invention mayallocate only the root sequence. In the case of using the ZCZ CAZACsequence due to the insufficient number of root sequences, the presentinvention may allow the CAZAC sequence to employ a specific sequencewhich is in an initial predetermined range or the last predeterminedrange from among total indexes. In this case, it should be noted thatthe term “predetermined range” can be established in different waysaccording to system detection performances.

In the case of comparing the above-mentioned method with the othermethod for allowing the ZCZ sequence not to be used in the cell havingthe high frequency offset, the above-mentioned method increasescategories or types of available sequences, so that there is almost noneed to perform the cell planning.

In more detail, if the number of total CAZAC sequences is Nt as shown inFIG. 3, the sequence to be used in the cell of the high frequency offsetmay be set to CAZAC indexes 0, 1, 2, Nt-2, Nt-1, and Nt.

In the meantime, in the case of using the CAZAC sequence for the cellhaving the frequency offset of more than the predetermined level, thereis no need to use only indexes other than the above-mentioned CAZACindexes 0, 1, 2, Nt-1, Nt-2, and Nt. In order to reduce the interferencebetween the aforementioned CAZAC sequence and the other sequence usedfor the cell having the high frequency offset, the present invention maynot use the sequence index sued for the cell having the high frequencyoffset as necessary, resulting in the implementation of high efficiency.

In the meantime, in the case of using the ZCZ sequence to guarantee thenumber of available sequences in the cell having the high frequencyoffset and/or to guarantee the performance of estimating the time delayoccurred in the channel, the present invention establishes the cyclicshift interval in the restricted case in consideration of the alias(i.e., Doppler shift) caused by the frequency offset. As a result, thepresent invention prevents the performance deterioration caused by thefrequency offset, and a detailed description thereof will hereinafter bedescribed.

If the presence of the frequency offset is decided, the frequencyresponse of the Rx signal can be represented by the above Equation 6.

In the meantime, Equation 6 shows that a signal value is transferredfrom all the neighboring sub-carriers due to the frequency offset.However, indeed, a specific component greatly affecting the channelresponse of the Rx signal may be set to a part located at both sides ofa corresponding sub-carrier, wherein the part receives a signal of theneighboring sub-carrier.

Therefore, in the case of considering only the first order case,Equation 6 may be represented by three terms, as shown in the followingequation 7:

r(k, f _(off))=p(−f₀ −f _(off))c(k−1)+p(−f _(off))c(k)+p(f−f_(off))c(k+1)   [Equation 7]

In the meantime, the reception end applies a conjugate complex numberc(n) to the Rx signal, so that the applying result can be represented bythe following equation 8:

$\begin{matrix}{{{r\left( {k,f_{off}} \right)}{c^{*}(k)}} = {\alpha_{0} + {\alpha_{- 1}{\exp \left( {- \frac{{j2\pi}\; {Mk}}{N}} \right)}} + {\alpha_{1}{\exp \left( \frac{{j2\pi}\; {M\left( {k + 1} \right)}}{N} \right)}}}} & \left\lbrack {{Equation}\mspace{14mu} 8} \right\rbrack\end{matrix}$

The pulse-shaping function of Equation 7 can be easily denoted by araised cosine- or sinc-function.

For the convenience of description, the pulse-shaping function isrepresented by constants α₀, α⁻¹, and α₁.

With reference to Equation 8, the channel response of the Rx signaloccurs at three points, i.e., “t” indicative of a target position in thetime domain, “t−M” indicative of a position shifted to the left side,and “t+M” indicative of a position shifted to the right side. It can berecognized that the channel response generated at the M-shifted positionon the basis of the right/left sides corresponds to the alias of the Rxsignal, i.e., the Doppler shift component having the 1-subcarrierspacing.

The above-mentioned phenomenon in which the alias occurs in the channelresponse due to the frequency offset is shown in FIG. 4.

FIG. 4 is a conceptual diagram illustrating aliases which occur in atime-domain channel response of a reception sequence due to thefrequency offset according to the present invention.

If the cyclic shift is applied to a sequence used in a specific cellhaving a frequency offset of more than a predetermined level, a singlechannel response occurs at the target position in the Rx-channelresponse of the corresponding sequence, and two additional aliases mayoccur in the Rx-channel response of the corresponding sequence accordingto the 1-subcarrier-spacing-sized Doppler shift.

Therefore, if the CS-applying interval is established irrespective ofthe target position and the alias positions, an unexpected overlappingoccurs between the channel response and the alias of the Rx sequence dueto the channel delay spreading and the propagation delay, so that theconfusion between the target position and the alias position may occuramong different CS-applying sequences.

Accordingly, if the restricted case is decided when the CS-applyinginterval is established in the CAZAC sequence, the present inventionconsiders the alias generated in the channel response, so that itestablishes the CS-applying interval during a specific period in whichthe channel response of the Rx sequence does not overlap with the aliasof the above channel response.

FIG. 4 shows an exemplary case in which the M-sized (where M=sequenceindex) alias occurs when CAZAC sequence is generated in a frequencydomain. However, if the CAZAC sequence is generated in the time domain,the alias generation position caused by the Doppler shift of the1-subcarrier spacing may be determined in different ways.

All the CS-applying cases used for the individual domains willhereinafter be described in detail.

For the convenience of description and better understanding of thepresent invention, FIGS. 5-11 assume that the cyclic shift unit is setto T₀.

FIG. 5 is a conceptual diagram illustrating a method for establishing anew cyclic shift (CS)—applying unit by adding an additional margin to anold CS-applying unit according to the present invention.

The present invention generates a cyclic-shifted preamble according tothe design based on the RACH component. However, under the environmentin which the OFDM frequency offset exists, the reception end of thepresent invention may easily mistake a normal sequence for anothersequence.

In order to prevent the above-mentioned problem from being generated,the present invention may use an additional cyclic shift margin as shownin FIG. 5.

Referring to FIG. 5, the delay spread is indicative of a channel delayspread, and the round trip delay (RTD) is indicative of a propagationproceeding time of a physical distance between the user equipment (UE)and the Node-B. In the case of using the additional cyclic shift margin,the present invention adjusts the margin size for each sequence, so thatit can reduce the influence of the frequency offset when the sequence isused.

In the case of implementing the frequency offset using the additionalmargin, the cyclic shift unit is decided by the function of the CAZACsequence. In other words, in association with the CAZAC sequence “M”,the cyclic shift unit is represented by the following equation 9:

T(M)=T ₀ +T _(margin)(M)   [Equation 9]

where T₀ is indicative of a common cyclic shift unit irrespective of thesequence index, and T_(margin) (M) is indicative of an additional marginused when the sequence index is M. This margin can be decided by othermethods according to usages of the sequence and the cyclic shift.

Therefore, although it is preferable that the cyclic shift unit is atleast 2M, this additional margin may be changed to another marginaccording to the CS-applying area. The above-mentioned situation isshown in FIGS. 6 and 7.

FIGS. 6 and 7 are conceptual diagrams illustrating application examplesof the additional margin of FIG. 5 under the condition that a sequenceindex is low according to the present invention.

Here, in case of FIG. 6, the interval of M due to the frequency offsetis smaller than the cyclic shift interval of T₀. Even when using thisrange, we can avoid the overlapping problem with other sequences.However, there may be a problem of estimating the information for thetime delay of the transmitted sequence. So, in one embodiment of thisinvention, it is preferable not using this range where the interval of Mdue to the frequency offset is smaller than the cyclic shift interval ofT₀. But, there may be a system using this range according to therequirement of the system.

The oblique-lined part of FIGS. 6 and 7 indicates the cyclic shiftopportunity.

If the signal having no influence of the frequency offset is located at“t”, the pulse affected by the frequency offset may occur at a singlepoint of the left side, and may occur at a single point of the rightside. If the signal includes T₀ used as a basic cyclic shift unit,T_(margin)(M) may be set to 2M.

The additional margin is applied to all the indexes, so that the presentinvention may define the cyclic shift highly resistant to thefrequency/timing offsets.

However, the higher the sequence index, the higher the value ofT_(margin)(M). As a result, the number of available cyclic shifts isreduced to “1”. In order to prevent the reduction of the cyclic shifts,the present invention will disclose the case of the high CAZAC index indetail.

FIGS. 8 and 9 are conceptual diagram illustrating exemplary additionalmargins of FIG. 5 under the condition that a sequence index is highaccording to the present invention.

FIG. 8 shows the case in which the CAZAC index “M” is 2T₀˜3T₀, and FIG.9 shows the case in which the CAZAC index “M” is 3T₀˜4T₀. Although thecase of FIG. 8 considers the basic cyclic shift unit, the cyclic shiftset denoted by the oblique-lined part may be additionally inserted inthe intermediate space. The case of FIG. 9 has a wider space, so that atleast two cyclic shifts can be inserted into this wider space.

FIG. 10 shows an example of a single group composed of P cyclic-shiftsets according to the present invention.

Referring to FIG. 10, if the above-mentioned explanation is generalized,slots denoted by the oblique-lined parts are defined in the 3M range inwhich the block is constructed by pulses, and the M range isPT₀˜(P+1)T₀, it can be recognized that P cyclic-shift-sets areconstructed.

For the convenience of description, the 3M or 2M+PT₀ unit willhereinafter be referred to as a cyclic shift group. A specific sequenceto which the cyclic shift is applied includes a predetermined number ofcyclic shift groups. The predetermined number of cyclic shifts can beapplied to each cyclic shift group, so that the predetermined number ofcyclic shifts can be applied to the cyclic shift component caused by theDoppler shift.

FIG. 11 is a conceptual diagram illustrating a method for establishing acyclic shift (CS)—applying group and the CS-applying interval of eachgroup according to the present invention.

Referring to FIG. 11, units of cyclic shift groups can be defined intotal sequences, and each cyclic shift group can be defined as shown inFIG. 10. Provided that the number of cyclic shift groups is G and thenumber of cyclic shifts for each group is P, the total number ofavailable cyclic shifts is P*G. As shown in FIG. 11, according to oneembodiment of the present invention, it is assumed that the sequence isdivided into groups, and each group searches for a restricted availablecyclic shift in each group.

In the case of using the above-mentioned scheme, all the availablecyclic shifts are defined in the index range in which the number ofcyclic shift groups is “1”. If the sequence length is N, this rangehaving the sequence length of N corresponds to indexes ranging from1˜N/3 to 2N/3˜N-1. In this case, the k-th index has the same cyclicshift group as that of the (N-k)-th index and the cyclic shift set.

FIG. 12 shows locations at which pulses occur by an interference whenthe CAZAC index is contained in the interval of N/3˜N/2 according to thepresent invention.

A single square of FIG. 12 indicates the cyclic shift unit. If the CAZACindex is higher than “N/3”, all the consecutive cyclic shift positions(i.e., the cyclic shift positions defined by T₀) cannot be used, andthey can be used according to predetermined rules.

A method for establishing the restricted cyclic shift set according toone embodiment of the present invention will hereinafter be described.

FIG. 13 is a flow chart illustrating a restricted cyclic shift setaccording to one embodiment of the present invention.

Referring to FIG. 13, if the restricted cyclic shift set is establishedin a cell having the frequency offset of more than a predeterminedthreshold value, the present invention provides a method forestablishing the cyclic shift in consideration of the aliasing, so thatthere is no confusion between a desired channel response and thisaliasing.

For this purpose, as shown in step S1301 of FIG. 13, the presentinvention provides a distance “d_(u)” between the response generated bythe Doppler shift and a desired channel response using a given sequenceroot index “u”. In this case, the above distance corresponds to thecyclic shift generated by the Doppler shift corresponding to the1-subcarrier spacing.

A detailed description of the variable “d_(u)” will hereinafter bedescribed in detail.

FIG. 14 is a conceptual diagram illustrating a method for establishing avariable (d_(u)) of a cyclic shift corresponding to the Doppler shiftassociated with the 1-subcarrier spacing when the restricted cyclicshift set is established according to the present invention.

Referring to FIG. 14( a), if there is no influence of the Dopplerfrequency, the peak position generated by the correlation operation ofthe reception end is denoted by “1401”. By the delay spread and theround trip delay (RTD), the peak position at the reception end appearsat the cyclic shift unit N_(CS) (1402) used as the cyclic shift unitbasically decided by the system.

In the meantime, in the case of the presence of the Doppler frequencycorresponding to the 1-subcarrier spacing, the peak position caused bythe correlation operation of the reception end is decided according tothe sequence indexes.

According to the present invention, the distance between the peakposition based on the Doppler shift corresponding to the 1-subcarrierspacing Δf and the ideal peak position is called “d_(u)”.

In other words, FIG. 14( b) shows the shift of the reception-end channelresponse caused by the Doppler frequency −Δf. FIG. 14( c) shows theshift of the reception-end channel response caused by the Dopplerfrequency +Δf. Based on the above-mentioned fact, the value “d_(u)” maybe considered to be the cyclic shift caused by the Doppler shift.

If the restricted cyclic shift is established in consideration of thecyclic shift corresponding to the Doppler shift of the 1-subcarrierspacing, the present invention controls the established restrictedcyclic shift not to be overlapped with the channel response movementcaused by the Doppler shift.

The present invention excludes the reserved areas “reserved” of FIGS.14( a) and 14(b) from the established cyclic shift interval, so that itcan prevent an unexpected confusion from being generated between channelresponses although the relatively high Doppler shift has occurred.

Referring back to FIG. 13, the present invention acquires secondaryvariables using the acquired variable “d_(u)” of the above step S1301 atstep S1302. Namely, the present invention acquires the number (G) ofcyclic shift groups, the number (P) of cyclic shifts applicable to eachgroup, and the length (S) of each group from current sequences (e.g., ZCsequences).

The above-mentioned secondary variables must be differently establishedaccording to sequence indexes, because the group length is changed toanother according to the sequence indexes. And, the variable “d_(u)” isdependent on the sequence index, so that the present invention providesa method for establishing secondary variables according to the range ofthe variable “d_(u)”.

Furthermore, the present invention may apply not only the abovegroup-based cyclic shift but also an additional cyclic shift using aspecific area which is not contained in the cyclic shift group withinthe sequence range, and a detailed description thereof will hereinafterbe described.

Thereafter, at step S1303, the present invention establishes the cyclicshift using the acquired secondary variables of step S1302.

The mathematical relationship between detailed variables for the cyclicshift application will be described in detail.

The restricted cyclic shift according to the present invention has beenproposed to prevent the high Doppler frequency effect from beinggenerated.

The other cyclic shift offset “C_(off)” different from the “d_(u)”variable will hereinafter be described in detail.

The “C_(off)” value indicates the degree of an offset generated by theDoppler shift. If the offset degree generated by the Doppler shift isless than the half of the given sequence range, this offset degree mayhave the same meaning as that of the d_(u) variable. Otherwise, if theoffset degree generated by the Doppler shift is equal to or higher thanthe half of the given sequence range, the resultant value acquired whenthe “C_(off) value is subtracted from the total sequence length maycorrespond to the d_(u) variable.

The “C_(off) value is dependent on the root index of the used sequence.The preamble may be generated from either the time domain or thefrequency domain. The relationship between “C_(off)” and “u” values isdependent on the domain generating the preamble.

If the ZC sequence is generated from the frequency domain, and thecyclic shift is applied in the time domain, the present invention mayinduce the “C_(off)” value using the following method, and a detaileddescription thereof will hereinafter be described.

It is assumed that the signal energy is propagated by the valuetransferred from the neighboring sub-carrier according to the Dopplerfrequency. And, it is assumed that the transferring from the neighboringcarrier occurs at only the sub-carrier position spaced from a currentsub-carrier by one blank, and this case is referred to as a first ordercase. In this case, the Rx signal at the specific sub-carrier iscomposed of three terms shown in the following equation 10:

s(n)=p(−f _(off))c(n)+p(−w ₀ −f _(off))c(n−1)+p(w ₀ −f _(off))c(n+1)  [Equation 10]

Where, the pulse-shaping function “p(f)” may be denoted by a raisedcosine- or sinc-function. For the convenience of description, ifconstants c₀, c⁻¹, and c₁ are established, the s(n) value can be denotedby s(n)=c₀c(n)+c⁻¹c(n−1)+c₁c(n+1). For the convenience of description,if the conjugate of the sequence is multiplied by the resultant values(n), the following equation 11 can be acquired:

s(n)c*(n)=c*(n)(c ₀ c(n)+c ⁻¹ c(n−1)+c _(i) c(n+1))=c ₀ +c ⁻¹c(n−1)c*(n)+c ₁ c(n+1)c*(n)   [Equation 11]

In Equation 11, if “c(n)=x(n)” is denoted by CAZAC, c(n−1)c*(n) can berepresented by the following equation 12:

$\begin{matrix}{{{x^{*}\left( {n - 1} \right)}{x(n)}} = {\exp \left( {- \frac{{j2\pi}\; {un}}{N_{ZC}}} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 12} \right\rbrack\end{matrix}$

Here, “u” indicates the root index, and “Nzc” indicates the sequencelength.

If Equation 12 is applied to Equation 11, it can be recognized that“s(n)” is composed of three signals. A first term of the “s(n)” value isindicative of a simple DC component, a second term is indicative of acomplex exponential wave having the frequency of u/Nzc, and a third termis indicative of a complex exponential wave having the frequency of−u/Nzc.

Therefore, the “C_(off)” value can be represented by the followingequation 13:

C_(off,u)=U   [Equation 13]

On the contrary, if the ZC sequence is generated from the time domainand the cyclic shift is generated from the time domain, the “C_(off)value can be calculated by the following method.

If the RACH preamble received without having the frequency offset is setto r(n), the RACH signal received along with the frequency offset can berepresented by the following equation 14:

{tilde over (r)}(n)=e ^(jΔwn) r(n)   [Equation 14]

Where Δω is denoted by Δω=2 πΔf/f_(S), and Δf indicates the frequencyoffset denoted by the hertz (Hz) unit, and f_(s) is indicative of asampling rate of the RACH preamble.

The auto-correlation of the {tilde over (r)}(n) value can be calculatedby the equation “r(n)=x_(u)(n)”, wherein “u” is indicative of the indexof the ZC sequence

$\begin{matrix}\begin{matrix}{{c_{r}(0)} = {\sum\limits_{n = 0}^{N_{ZC} - 1}{{\overset{\sim}{r}(n)}{x_{u}^{*}(n)}}}} \\{= {\sum\limits_{n = 0}^{N_{ZC} - 1}^{j\; \Delta \; {wn}}}} \\{= {\sum\limits_{n = 0}^{N_{ZC} - 1}^{j\; 2{\pi {({\Delta \; {f/f_{Z}}})}}n}}}\end{matrix} & \left\lbrack {{Equation}\mspace{14mu} 15} \right\rbrack\end{matrix}$

In Equation 15, if “C_(off,u)” is indicative of the margin of afrequency offset, the auto-correlation of {tilde over (r)}(n) can becalculated by r(n)=x_(u)((n+c_(off,u))_(N) _(ZC) ) of the followingequation 16:

$\begin{matrix}\begin{matrix}{{c_{r}(0)} = {\sum\limits_{n = 0}^{N_{ZC} - 1}{{\overset{\sim}{r}(n)}{z_{v}^{*}(n)}}}} \\{= {\sum\limits_{n = 0}^{N_{ZC} - 1}^{j\; 2{\pi {({{({u \cdot c_{{off},u}})}_{N_{ZC}}/N_{ZC}})}}n}}}\end{matrix} & \left\lbrack {{Equation}\mspace{14mu} 16} \right\rbrack\end{matrix}$

In Equation 16, “( )_(Nzc)” is indicative of a modular operation of the“Nzc” value. If C_(off,u)′=u*C_(off,u) is a root index related with thesampling shifts, and γ is indicative of a re-sampling ratio replying tothe timing error, the C_(off,u)′ value can be denoted byc_(off,u)′=(γ−1)N_(ZC).

By Equations 15 and 16, the γ value can be denoted by γ=1+Δf/f_(S).

The channel response position is called a main lobe, and the aliasresponse position of a channel affected by the (+/−) Doppler frequencyis called a side lobe.

In more detail, the main lobe is indicative of the position caused bythe 0 offset, and is equal to a normal channel response position whenthere is no influence of the Doppler frequency.

The positive(+) side lobe is indicative of the position caused by thepositive(+) offset, and is equal to an alias response position affectedby the positive (+) Doppler frequency. The negative(−) side lobe isindicative of the position caused by the negative(−) offset, and isequal to an alias response position affected by the negative(−) Dopplerfrequency.

As can be seen from Equation 16, it can be recognized that the main lobeof the auto-correlation peak occurs at C_(off,u)=0 or C_(off,u)′=0. Bythe above Equation 16, the pair of side-lobes occurs under the conditionof the following equation 17:

(u*C _(off,u))_(Nzc)=−1   [Equation 17]

Therefore, the result of “u*C_(off,u)−m*Nzc” is equal to “−1”, asrepresented by “C_(off,u)=(m*Nzc−1)/u”. In this case, “m” is indicativeof the lowest integer capable of allowing the C_(off,u) value to be aninteger. For example, if the ZC-sequence length is 839 and the rootindex is 300, the “m” value is set to 59, and the C_(off,u) value is setto 165.

In the case of using the ZC sequence in the time domain, the C_(off)value can be defined by the following equation 18:

C _(off,u)=(N _(zc) m−1)/u   [Equation 18]

In Equation 18, “m” is indicative of the smallest positive numbercapable of allowing the C_(off) value to be an integer, and “Nzc” isindicative of the ZC length,

All the indexes “u” is a relative prime of the Nzc value. Therefore, thepositive integer number (u_(inv)=1/u) capable of satisfying the equation(u*u_(inv)=1 mod Nzc) exists. Therefore, the C_(off,u) value can beeasily represented by the following equation 19:

$\begin{matrix}{c_{{off},u} = {{\frac{m \cdot N_{ZC}}{u} - \frac{1}{u}} = {u^{- 1}{mod}\; N_{ZC}}}} & \left\lbrack {{Equation}\mspace{14mu} 19} \right\rbrack\end{matrix}$

In Equation 19, a negative sign (−) is the opposite of the positive sign(+), so that it can be represented by the following equation 20:

C _(off,u)=(1/u) mod N _(zc)   [Equation 20]

In brief, if the CAZAC sequence is used in the frequency domain, theCAZAC-sequence index “u” becomes “C_(off)” without any change. If theCAZAC sequence is used in the time domain, the “(1/u) mod Nzc” isperformed on the index “u” of the CAZAC sequence, so that the C_(off)value can be acquired.

Provided that the ZC sequence is used in the frequency or time area, andthe conjugate property between the C_(off) and ZC sequences is used, thedistance “d_(u)” between the main-lobe and the side-lobe can berepresented by the following equation 21:

$\begin{matrix}{d_{u} = \left\{ \begin{matrix}{c_{{off},u},} & {u \leq {N_{ZC}/2}} \\{{N_{ZC} - c_{{off},u}},} & {u > {N_{ZC}/2}}\end{matrix} \right.} & \left\lbrack {{Equation}\mspace{14mu} 21} \right\rbrack\end{matrix}$

The present invention provides a variety of methods in establishing therestricted cyclic shifts, for example, a first method for establishingthe restricted cyclic shift without using the fixed cyclic shiftposition, and a second method for establishing the restricted cyclicshift using the fixed cyclic shift position.

The first method is associated with the restricted cyclic shift withoutconsidering the pre-defined shift position. The second method isassociated with the restricted cyclic shift with the consideration ofthe pre-defined shift position.

In regard to the first method, there are a variety of methods, i.e., amethod for directly using the shift value of the V_(a)-th restrictedcyclic shift, and a method for establishing the cyclic shift intervalusing the shift value “C_(va)”. Namely, the cyclic-shifted sequencebecomes x_(u,v)(n)=x_(u)((n+C_(Va)) mod N_(zc)) as shown in Equation 4.

In regard to the first method, there are a variety of methods employinga decimal “V_(a)” for use in the cyclic shift, for example, a method forestablishing the cyclic shift interval by calculating the shift-indexdecimal V_(a).

In other words, if the length of the cyclic shift is set to Ncs, thecyclic-shifted index becomes “x_(u,Va)(n)=x_(u)((n+round(v_(a)N_(cs)))mod N_(zc))”. In this case, “round” is indicative of a round-offfunction.

In regard to the second method, there are a variety of methods employingthe integer “V_(a)” for use in the cyclic shift, for example, a methodfor establishing the cyclic shift interval by calculating theshift-index integer V_(a). Namely, the cyclic-shifted sequence becomesx_(u,Va)(n)=x_(u)((n+v_(a)N_(cs)) mod N_(zc)).

In the meantime, if the cyclic shift is performed by the multiple ofNcs, random access preambles, each of which has the zero correlationzone (ZCZ) area having no correlation in the u-th root ZC sequence, aredefined by x_(u,v)(n)=x_(u)((n+vN_(cs)) mod N_(zc)). This definition isappropriate for the low/middle cell having no problem in the highfrequency offset. However, if the restricted cyclic shift is used in thehigh-mobility cell, the above-mentioned definition is inappropriate forthe high-mobility cell. Specifically, the available “v” value isrestricted, and the number of available ZCZ preambles is reduced to ⅓ ofthe ZCZ preambles of a general case.

Embodiments associated with the above-mentioned cases will hereinafterbe described in detail.

Best Mode

This embodiment of the present invention will disclose a method forestablishing the restricted cyclic shift using only the influence of theDoppler shift, without using the fixed cyclic shift position.

The present invention assumes that the preamble is generated using theZC sequence used as the CAZAC sequence.

The “d_(u)” value of the following equation 22 shows a specific case inwhich the

ZC sequence is generated in the frequency domain.

$\begin{matrix}{d_{u} = \left\{ \begin{matrix}{u,} & {0 \leq u < {N_{ZC}/2}} \\{{N_{ZC} - u},} & {{N_{ZC}/2} \leq u < N_{ZC}}\end{matrix} \right.} & \left\lbrack {{Equation}\mspace{14mu} 22} \right\rbrack\end{matrix}$

In the case of generating the ZC sequence in the time domain, the“d_(u)” value can be represented by the following equation 23:

$\begin{matrix}{d_{u} = \left\{ \begin{matrix}{{\left( {{N_{ZC} \cdot m} - 1} \right)/u},} & {0 \leq \left( {u^{- 1}{mod}\; N_{ZC}} \right) < {N_{ZC}/2}} \\{{N_{ZC} - {\left( {{N_{ZC} \cdot m} - 1} \right)/u}},} & {{N_{ZC}/2} \leq \left( {u^{- 1}{mod}\; N_{ZC}} \right) < N_{ZC}}\end{matrix} \right.} & \left\lbrack {{Equation}\mspace{14mu} 23} \right\rbrack\end{matrix}$

In Equation 23, “m” is indicative of the smallest positive numbercapable of allowing the “d_(u)” value to be an integer, and Nzc isindicative of the ZC length. Equation 23 can also be represented by thefollowing equation 24:

$\begin{matrix}{d_{u} = \left\{ \begin{matrix}{{u^{- 1}{mod}\; N_{ZC}},} & {0 \leq \left( {u^{- 1}{mod}\; N_{ZC}} \right) < {N_{ZC}/2}} \\{{N_{ZC} - \left( {u^{- 1}{mod}\; N_{ZC}} \right)},} & {{N_{ZC}/2} \leq \left( {u^{- 1}{mod}\; N_{ZC}} \right) < N_{ZC}}\end{matrix} \right.} & \left\lbrack {{Equation}\mspace{14mu} 24} \right\rbrack\end{matrix}$

Therefore, the v-th cyclic shift of the u-th root index can be definedby x_(u,v)(n)=x_(u)((n+C_(v)) mod N_(zc)). In this case, if the generalcyclic shift is decided, the C_(v) value can be represented byC_(v)=v*N_(cs). If the restricted cyclic shift is decided, the C_(v)value can be represented by the following equation 25.

$\begin{matrix}{C_{v} = \left\{ \begin{matrix}{{v \cdot N_{CS}},} & {{v = 0},1,K,\left( {\left\lfloor {N_{ZC}/N_{CS}} \right\rfloor - 1} \right),} & {{for}\mspace{14mu} {unrestricted}\mspace{14mu} {sets}} \\{{{S \cdot \left\lfloor {v/P} \right\rfloor} + {\left( {v\; {mod}\; P} \right) \cdot N_{CS}}},} & {{v = 0},1,K,\left( {{P \cdot G} + R - 1} \right),} & {{for}\mspace{14mu} {restricted}\mspace{14mu} {sets}}\end{matrix} \right.} & \left\lbrack {{Equation}\mspace{14mu} 25} \right\rbrack\end{matrix}$

If the restricted cyclic shift having no pre-defined shift position isdecided, this case is considered to be a first case (Case 1), and adetailed description thereof will hereinafter be described.

The u-th root ZC sequence and the v-th random access preamble, each ofwhich has the zero correlation area, are defined by“x_(u,V)(n)=x_(u)((n+C_(V)) mod N_(zc))”.

In this case, “C_(v)” is denoted by the above equation 25.

In other words, in the case of the unrestricted sets having a smallamount of the Doppler-shift influence, the present invention mayestablish the cyclic shift corresponding to an integer multiple of Ncsequal to the basic cyclic shift unit.

However, the case of the unrestricted sets less affected by the Dopplershift may establish the cyclic shift corresponding to the integermultiple of Ncs.

In association with FIG. 13, the case of the restricted sets greatlyaffected by the Doppler shift may establish the number (G) of cyclicshift groups, the number (P) of cyclic shifts applicable to each cyclicshift group, and the number (R) of additional cyclic shifts.

The method for calculating each secondary variable may be differentlydecided by the “d_(u)” range as previously stated in FIG. 13. During thealias distance interval of Ncs≦d_(u)<(Nzc/3), the number of cyclicshifts per group is denoted by P=└d_(u)/N_(CS)┘, and there areG(G=└N_(ZC)/S┘) groups, each of which has the length S=2·d_(u)+P·N_(CS),and the number of restricted additional cyclic shifts is denoted byR=max(└(N_(ZC)−2·d_(u)−G·S)/N_(CS)┘, 0).

During the alias distance interval of (Nzc/3)≦d_(u)≦(Nzc−Ncs)/2, thenumber of cyclic shifts per group is denoted byP=└(N_(ZC)−2·d_(u))/N_(CS)┘, and there are G(G=└d_(u)/S┘) groups, eachof which has the length S=N_(ZC)−2·d_(u)+P·N_(CS), and the number ofrestricted additional cyclic shifts is denoted byR=min(max(└(d_(u)−G·S)/N_(CS)┘, 0), P).

The principles for calculating the above-mentioned secondary variableswill hereinafter be described in detail.

d_(u)<N_(CS)   (1)

FIG. 15 is a conceptual diagram illustrating a specific case in whichthe variable (d_(u)) is less than a basic unit N_(CS) to which thecyclic shift (CS) is applied according to the present invention.

The cyclic shift unit (N_(CS)) is designed in consideration of the delayspread and the RTD which are capable of being generated in the channel.Therefore, if d_(u) is less than N_(cs), a peak caused by the delayspread and/or the RTD within the N_(CS) range may overlap with the otherpeak caused by the Doppler shift, as shown in FIG. 15. Therefore, whenestablishing the restricted cyclic shift, this embodiment does notestablish the cyclic shift for the case in which the d_(u) value is lessthan the N_(cs) value.

N _(CS)≦d_(u)<(N_(ZC)/3)   (2)

FIG. 16 is a conceptual diagram illustrating a method for calculating avariable establishing the cyclic shift within the interval ofN_(CS)≦d_(u)<(N_(ZC)/3) according to the present invention.

As shown in FIG. 16, the cyclic shift area generated by the Dopplerfrequency occurs in the interval of N_(CS)≦d_(u)<(N_(ZC)/3).Specifically, the cyclic shift area appears in the range of a sequencelength located at both sides of the intended cyclic shift.

According to this embodiment, the cyclic shift areas caused by theDoppler frequency of both sides of the cyclic shift may be grouped intoa single group. Also, the present invention determines how many Ncsvalues can be used without overlapping with others within the “d_(u)”range. The number of restricted cyclic shifts available for each groupmay be set to P. Namely, the P value can be calculated by the followingequation 26:

P=└ _(u) /N _(CS)┘  [Equation 26]

The distance between a specific channel response 1601 and the alias 1601a caused by the Doppler shift is denoted by “d_(u)”. The distancebetween the specific channel response 1601 and the other alias 1601 bcaused by the Doppler shift is denoted by “d_(u)”.

If the P cyclic shifts are applied to each group, aliases generated inthe left area on the basis of the channel response 1601 are contained inthe d, range, and other aliases generated in the right area on the basisof the channel response 1601 may exist outside of the d_(u) range.

In this case, in the case of considering all the aliasing operations ofP channel responses generated in the right area, a corresponding lengthcorresponds to P·N_(CS) (1602).

Therefore, the length (S) of a single cyclic shift group may be equal tothe sum of the “d_(u)” length and the “P·N_(CS)” length, and isrepresented by the following equation 27:

S=2·d _(u) −P·N _(CS)   [Equation 27]

In the meantime, the number of cyclic shift groups in total sequencesmay be calculated by dividing the total sequence length (N_(zc)) by thegroup length (S), and can be represented by the following equation 28:

G=└N _(ZC) /S┘  [Equation 28]

In the meantime, as shown in FIG. 16, a specific area 1603 less than thegroup length (S) may be left. The length of the “1603” area correspondsto “N_(ZC)−G·S”, where N_(ZC) is the length of an overall sequence, G isthe number of groups, and S is the group length.

If N_(ZC)−G·S−2d_(u) is higher than N_(CS), the additional cyclic shiftmay also be applied to the above-mentioned area 1603, and a detaileddescription thereof is shown at the “1604” area of FIG. 16. Therefore,provided that the number of cyclic shifts which are not based on thecyclic shift group is R, the R value can be represented by the followingequation 29:

R=max(└(N _(ZC)−2·d _(u) −G·S)/N _(CS)┘, 0)   [Equation 29]

(N _(ZC)/3)≦d _(u)<(N _(ZC) −N _(CS))/2   (3)

FIG. 17 is a conceptual diagram illustrating a method for calculating avariable establishing the cyclic shift within the interval of(N_(ZC)/3)≦d_(u)<(N_(ZC)−N_(CS))/2 according to the present invention.

In the area of (N_(ZC)/3)≦d_(u), differently from the above-mentioned(2) case (i.e., the aforementioned (2) case of N_(CS)≦d_(u)<(N_(ZC)/3)),positions of the channel response and the aliasing caused by the Dopplershift exceed the total sequence length N_(ZC), so that the aliasing mayoccur between the channel response of the ideal case and the d_(u)range.

For example, the peak located at the “1701” position of FIG. 17 thealiasing may occur at positions 1701 a and 1701 b by the (+/−) Dopplershift. Therefore, the number of cyclic shifts applicable to a singlecyclic shift group in this (3) case is decided by the “N_(ZC)−2d_(u)”area (1702) located at the center of FIG. 17, so that the number P ofrestricted cyclic shifts applicable to each group can be calculated bythe following equation 30:

P=└(N _(ZC)−2·d _(u))/N _(CS)┘  [Equation 30]

In this (3) case, the length S of each cyclic shift group can berepresented by the following equation 31:

S=N _(ZC)−2·d _(u) +P·N _(CS)   [Equation 31]

The variable S is equal to the sum of the length of the 1702 area(N_(ZC)−2d_(u)) and the length of the 1703 area corresponding to the“P·N_(CS)” length. The “P·N_(CS)” length is variable with the number ofcyclic shifts applicable to each real group located at the right side

In the meantime, the above-mentioned (3) case determines the number ofcyclic shift groups in a given ZC sequence by considering how manylengths (S, where S=the length of a specific group) will be permitted inthe d_(u) range (1704), whereas the above-mentioned (2) case hasdetermined the number of cyclic shift groups in such a given ZC sequenceby considering how many lengths (S) will be permitted in the totalsequence length Nzc.

The spacing between a specific channel response and two aliases of thischannel response exceeds the total sequence range, so that the presentinvention controls the individual aliases not to overlap with each otherwithin the d_(u) range. The number of cyclic shift groups can berepresented by the following equation 32:

G=└d _(u) /S┘  [Equation 32]

Finally, the cyclic shift group is established in the d_(u) range (1704)as described above, and the 1705 area having the length shorter thanthat of the cyclic shift group may be left. This length of the 1705 areacorresponds to “d_(u)−G·S”. If the length of the 1705 area is longerthan N_(cs), the additional cyclic shift may be applied to this length.

Therefore, the number R of additional cyclic shifts can be representedby max(└(d_(u)−G·S)/N_(CS)┘).

If the length (S) of each cyclic shift group is higher than “P”, theadditional cyclic shifts corresponding to the number of more than “P”may overlap with the (+/−) aliasing area in the right area. Therefore,this embodiment may indicate the number R of additional cyclic shifts asshown in the following equation 33:

R=min(max(└(d _(u) −G·S)/N _(CS)┘, 0), P)   [Equation 33]

(N _(ZC) −N _(CS))/2≦d _(u)   (4)

Referring to FIG. 17, the N_(ZC)−2d_(u) area (1702) located at thecenter part must be larger than N_(cs), so that the cyclic shift can beapplied to each group. Namely, this requirement can be represented byN_(ZC)−2d_(u)>N_(CS).

If the above-mentioned requirement is represented in different ways onthe basis of the d_(u) value, it can be recognized that the equationN_(ZC)−N_(CS)>2d_(u) (i.e., (N_(ZC) −N _(CS))/2>d_(u)) must besatisfied. Therefore, this embodiment does not establish the restrictedcyclic shift in the range of (N_(ZC)−N_(CS))/2≦d_(u).

Based on the above-mentioned explanation of the individual intervals, adetailed description of only the restricted set contained in Equation 25will hereinafter be disclosed. Firstly, the restricted set of Equation25 can be represented by the following equation 34.

C _(v) =S·└v/P┘+(v mod P)·N_(CS) , v=0, 1, . . . , (P·G+R−1)   [Equation34]

The individual terms for use in the above cyclic shift will hereinafterbe described.

In Equation 34, S·└v/P┘ is indicative of a start point of each cyclicshift group. If the ν value is less than the number P of cyclic shiftsfor each group, S·└v/P┘ is indicative of “0”. If the ν value is higherthan the number P of cyclic shifts for each group and is less than “2P”,S·└v/P┘ is indicative of “S” corresponding to the length of a singlecyclic shift group.

If the ν value is higher than “2P” and is less than 3P, S·└v/P┘ isindicative of “2S” corresponding to the length of two cyclic shiftgroups.

(v mod P)·N_(CS) is indicative of the position of the cyclic shiftapplied to each group (or the position of an additional cyclic shift).In other words, the ν value is shifted to another position by apredetermined distance N_(cs) at intervals of the P time.

The ν value of Equation 34 (or Equation 25 including Equation 34) doesnot discriminate between the groups or components of the groups, and isindicative of the total number of cyclic shifts. As a result, the totalnumber of cyclic shifts can be represented by P·G+R.

MODIFIED EXAMPLES

A variety of modified examples applicable to the present invention willhereinafter be described.

Although the above-mentioned best mode has disclosed the specific casein which there is no restriction in the start point of the cyclic shift,the present invention can be applied to not only the above-mentionedcase but also other restricted cases.

Not only the above-mentioned best mode, but also all the embodimentscapable of being more generally applied to the present invention willhereinafter be described.

The position at which the alias occurs by the (+) Doppler frequency isdenoted by the “+offset” position, and the position at the alias occursby the (−) Doppler frequency is denoted by “−offset” position.

FIGS. 18 and 19 are conceptual diagrams illustrating a method forreducing the number of ZCZ preamble sequences due to an alias responsein the case of Nzc=839, Ncs=100, and d_(u)=155 according to the presentinvention.

The cyclic shift of FIG. 18 can begin at any position. The cyclic shiftof FIG. 19 can be performed at only the N_(cs)-multiple position. TheN_(cs) value of FIG. 18 is equal to that of FIG. 19, however, startpositions of the individual cyclic shifts are different in FIGS. 18 and19.

In conclusion, the case of FIG. 18 can construct many more cyclic shiftsthan those of FIG. 19. In more detail, the case of FIG. 18 eliminatesthe restriction of the start position of the cyclic shift, so that itcan acquire the additional restricted cyclic shift.

FIG. 20 is a conceptual diagram illustrating the increasing ratio of anavailable restricted cyclic shift after the restriction of a startlocation of the cyclic shift is removed in the case of Nzc=839 accordingto the present invention;

The elimination of the restriction in the cyclic shift starting may notincrease the hardware complexity.

Therefore, the restricted cyclic shift having no consideration in thepre-defined shift position is preferred, and the above-mentioned bestmode is established under the aforementioned assumption.

However, the present invention can also be applied to the restrictedcyclic shift having the pre-defined shift position, so that thefollowing description will disclose the above-mentioned two cases.

Firstly, the restricted cyclic shift case (i.e., Case 1) having noconsideration in the pre-defined shift position will hereinafter bedescribed.

Equation 21 indicates the alias distance, irrespective of the preamblegeneration domain. The number of restricted available cyclic shifts perroot ZC sequence is differently decided according to the root index andthe N_(cs) value, so that different equations for use in differentalias-distance ranges are required.

Specificall, there are two alias-distance ranges in which there is nodiscrimination between alias responses. The range in which therestricted cyclic shift can be used is set to Ncs≦d_(u)≦(Nzc−Ncs)/2. Inthis range, the cyclic shift range and two alias ranges are notoverlapped with each other.

In this case, if the preamble is generated in the frequency domain, the“d_(u)” value is set to “u” as denoted by d_(u)=u. If the preamble isgenerated in the time domain, the “d_(u)” value is set to “1/u mod Nzc”as denoted by d_(u)=1/u mod Nzc. The number of restricted cyclic shiftscan be represented by the following equation 35:

$\begin{matrix}{{N_{shift}\left( d_{u} \right)} = \left\{ \begin{matrix}{{{P \cdot G} + R},} & {{{for}\mspace{14mu} N_{CS}} \leq d_{u} \leq {\left( {N_{ZC} - N_{CS}} \right)/2}} \\{0,} & {o/w}\end{matrix} \right.} & \left\lbrack {{Equation}\mspace{14mu} 35} \right\rbrack\end{matrix}$

In Equation 35, “P” is indicative of the number of restricted cyclicshifts per group, “G” is indicative of the number of groups generated ina single preamble sequence, and “R” is indicative of the number ofrestricted additional cyclic shifts which is not based on the additionalgroup.

The available range of the restricted cyclic shift is denoted byNcs≦d_(u)≦(Nzc−Ncs)/2. This interval “Ncs≦d_(u)≦(Nzc−Ncs)/2” can bedivided into “Ncs≦d_(u)<(Nzc/3)” and “(Nzc/3)≦d_(u)≦(Nzc−Ncs)/2” on thebasis of Nzc/3.

The reason why the alias-distance range is divided into“Ncs≦d_(u)<(Nzc/3)” and “(Nzc/3)≦d_(u)≦(Nzc−Ncs)/2” on the basis ofNzc/3 has already been disclosed.

Therefore, “Ncs≦d_(u)≦(Nzc−Ncs)/2” is differently decided on the basisof “Nzc/3”. The range of Ncs≦d_(u)<(Nzc/3) and the range of(Nzc/3)≦d_(u)≦(Nzc−Ncs)/2 will hereinafter be described.

If the start position of the first group is set to “0”, the V_(a)-threstricted cyclic shift range is defined by [C_(Va, start), C_(Va, end)]in Equations 36 and 37.

$\begin{matrix}{C_{v_{a},{start}} = \left\{ \begin{matrix}{{{g \cdot S} + {p \cdot N_{CS}}},} & \begin{matrix}{{{{for}\mspace{14mu} v} = {{P \cdot g} + p}},} \\{{p = 0},1,\ldots \mspace{14mu},{P - 1},} \\{{g = 0},1,K,{G - 1}}\end{matrix} \\{{{G \cdot S} + {r \cdot N_{CS}}},} & \begin{matrix}{{{{for}\mspace{14mu} v} = {{P \cdot G} + r}},} \\{{r = 0},1,\ldots \mspace{14mu},{R - 1}}\end{matrix}\end{matrix} \right.} & \left\lbrack {{Equation}\mspace{14mu} 36} \right\rbrack \\{C_{{Va},{end}} = {C_{{Va},{start}} + {Ncs} - 1}} & \left\lbrack {{Equation}\mspace{14mu} 37} \right\rbrack\end{matrix}$

The alias occurs at the positions of the following equations 38 and 39:

F _(v) _(a) _(,start) ^(±)(d _(u))=(C _(v) _(a) _(,start) ±d _(u))_(N)_(ZC)   [Equation 38]

F _(v) _(a) _(,end) ^(±)(d _(u))=(C _(v) _(a) _(,end) ±d _(u))_(N) _(ZC)  [Equation 39]

In Equation 39, “( )_(Nzc)” is indicative of a modular operation.

Firstly, the alias-distance range Ncs≦d_(u)<(Nzc/3) (i.e., thealias-distance range 1) has G=└N_(ZC) /S┘ number of groups. Each groupincludes P=└d _(u)/N_(CS)┘ number of restricted cyclic shifts. Thelength of each group is denoted by S=2·d_(u)−P·N_(CS). If the availableadditional cyclic shift is a positive(+) number, the R value is denotedby R=└(N_(ZC)−G·S−2·d_(u))/N_(CS)┘.

FIG. 21 is a conceptual diagram illustrating an exemplary cyclic shiftin the case of Nzc=839, Ncs=40, and d_(u)=150 according to oneembodiment of the present invention. Each group has three cyclic shifts,and two additional cyclic shifts exist in the remaining ranges. In thisexample, the total number of restricted cyclic shifts is “5”.

According to one embodiment, the present invention applies the number ofcalculated groups, the number of restricted cyclic shifts per group, andthe group length to Equations 36 and 37, and then establishes the cyclicshift-applying interval in consideration of the above-mentionedparameters.

Next, in the alias-distance range (Nzc/3)≦d_(u)≦(Nzc−Ncs)/2 (i.e., thealias-distance range 2), the number of available cyclic shifts per groupis denoted by P=└(N_(ZC)−2·d_(u))/N_(CS)┘, the length of each group isdenoted by S=N_(ZC) −2·d _(u)+P·N_(CS), and there are G groups (whereG=└d_(u)/S┘).

The additional cyclic shift is selected from among the center part andthe residual part of the right side. In this case, the selected cyclicshifts should be the smallest number of cyclic shifts. Namely, if the Rvalue is a positive number, the number of additional cyclic shifts isdenoted by R=min(└(d_(u)−G·S)/N_(CS)┘, P). The start position of theVa-th restricted cyclic shift is calculated by applying theabove-mentioned parameters to Equations 36 and 37.

FIG. 22 is a conceptual diagram illustrating an exemplary cyclic shiftin the case of Nzc=839, Ncs=40, and d_(u)=399 according to oneembodiment of the present invention. Each group

There are four groups, each of which has a single cyclic shift and asingle additional cyclic shift. In this example, the total number ofrestricted cyclic shifts is 5.

According to this embodiment, the present invention applies the numberof calculated groups, the number of restricted cyclic shifts per group,and the group length to Equations 36 and 37, and then establishes thecyclic shift-applying interval in consideration of the above-mentionedparameters.

Indeed, the equal sing (=) between two alias distance ranges may have nomeaning or the relatively-low importance. For example, in the case ofusing the ZC sequence having the length of 839, the (Nzc/3) value isequal to 279.67 (i.e., (Nzc/3)=279.67), so that the divided rangesNcs≦d_(u)<(Nzc/0) and (Nzc/3)≦d_(u)≦(Nzc−Ncs)/2 may have the sameresults as those of the divided ranges Ncs≦d_(u)≦(Nzc/3) and(Nzc/3)<d_(u)≦(Nzc−Ncs)/2.

Next, the restricted cyclic shift (i.e., Case 2) considering thepre-defined shift position will hereinafter be described.

A method for generating the restricted cyclic shift using thepre-defined shift position is changed to another method. Eachalias-distance range includes not only G groups, each of which has Pcyclic shifts, but also a first additional cyclic shift out of the R₁groups.

In the case of using the pre-defined shift position, the presentinvention has a particular additional cyclic shift, differently from theother case in which no pre-defined shift position exists in thealias-distance range 2-area.

In the alias-distance range 2-area, the main region generally appears inthe front samples of the sequence, and the alias regions generallyappear in the rear samples of the sequence. However, according to theCase 2, the main region appears in the rear samples of the sequence, andthe alias regions appear in the front samples of the sequence.

The second additional cyclic shift is denoted by R₂. The secondadditional cyclic shift does not appear in the alias-distance range 1.The total number of restricted cyclic shifts can be represented by thefollowing equation 40:

$\begin{matrix}{{N_{shift}\left( d_{u} \right)} = \left\{ \begin{matrix}{{{P \cdot G} + R_{1} + R_{2}},} & {{{for}\mspace{14mu} N_{CS}} \leq d_{u} \leq {\left( {N_{ZC} - N_{CS}} \right)/2}} \\{0,} & {o/w}\end{matrix} \right.} & \left\lbrack {{Equation}\mspace{14mu} 40} \right\rbrack\end{matrix}$

Provided that the start position of the first group is “0”, the V_(a)-threstricted cyclic shift is defined in [C_(Va, start), C_(Va, end)] asdenoted by Equations 41 and 42:

$\begin{matrix}{C_{v_{a},{start}} = \left\{ \begin{matrix}{{{g \cdot S} + {p \cdot N_{CS}}},} & \begin{matrix}{{{{for}\mspace{14mu} v} = {{P \cdot g} + p}},} \\{{p = 0},1,\ldots \mspace{14mu},{P - 1},} \\{{g = 0},1,K,{G - 1}}\end{matrix} \\{{{G \cdot S} + {r_{1} \cdot N_{CS}}},} & \begin{matrix}{{{{for}\mspace{14mu} v} = {{P \cdot G} + r_{1}}},} \\{{r_{1} = 0},1,\ldots \mspace{14mu},{R_{1} - 1}}\end{matrix} \\\begin{matrix}{\left\lceil {\left( {N_{2\; C} - d_{u} + {P \cdot N_{CS}} + {\left( {G - 1} \right)S}} \right)/N_{CS}} \right\rceil \cdot} \\{{N_{CS} + {r_{2} \cdot N_{CS}}},}\end{matrix} & \begin{matrix}{{{{for}\mspace{14mu} v} = {{P \cdot G} + R_{1} + r_{2}}},} \\{{r_{2} = 0},{1\mspace{14mu} \ldots}\mspace{14mu},{R_{2} - 1}}\end{matrix}\end{matrix} \right.} & \left\lbrack {{Equation}\mspace{14mu} 41} \right\rbrack \\{\mspace{79mu} {C_{{Va},{end}} = {C_{{Va},{start}} + N_{CS} - 1}}} & \left\lbrack {{Equation}\mspace{14mu} 42} \right\rbrack\end{matrix}$

The related alias occurs at positions of the following equations 43 and44:

F _(v) _(a) _(,start) ^(±)(d _(u))=(C _(v) _(a) _(,start) ±d _(u))_(N)_(ZC)   [Equation 43]

F _(v) _(a) _(,end) ^(±)(d _(u))=(C _(v) _(a) _(,end) ±d _(u))_(N) _(ZC)  [Equation 44]

In Equations 43 and 44, ( )_(Nzc) is indicative of a modular operation.

In the alias-distance range Ncs≦d_(u)<(Nzc/3) (i.e., the alias-distancerange 1), G groups (where, G=└N_(ZC)/S┘) exists, P restricted cyclicshifts (where, P=└d_(u)/N_(CS)┘) exists, and the group length is denotedby If the R₁ value is a positive(+) number, the number of the firstadditional cyclic shifts is denoted by R₁=└(N_(ZC)−G·S−2·d_(u))/N_(CS)┘.

FIG. 23 is a conceptual diagram illustrating an exemplary cyclic shiftin the case of Nzc=839, Ncs=40, and d_(u)=150 according to anotherembodiment of the present invention. In FIG. 23, each group includesthree cyclic shifts and two cyclic shifts. In this example, the totalnumber of restricted cyclic shifts is “5”.

According to this embodiment, the present invention applies the numberof calculated groups, the number of restricted cyclic shifts per group,and the group length to Equations 41 and 42, and then establishes thecyclic shift-applying interval in consideration of the above-mentionedparameters.

Next, in the alias-distance range (Nzc/3)≦d_(u)≦(Nzc−Ncs)/2 (i.e., thealias-distance range 2), the number of available cyclic shifts per groupis denoted by P=└(N_(ZC)−2·d_(u))/N_(CS)┘, the length of each group isdenoted by S=(┌(N_(ZC)−2·d_(u))/N_(CS)┐+P)·N_(CS), and there are Ggroups (where G=└d_(u)/S┘).

The first additional cyclic shift is calculated by the same method asthat of the alias-distance range 1. If the R₁ value is a positivenumber, the number of first additional cyclic shifts is denoted byR=min(└(d_(u)−G·s)/N_(CS)┘, P).

If the R₁ value is equal to “0” (i.e., R₁=0), the presence or absence ofa second additional cyclic shift must be determined. The shape of thesecond additional cyclic shift is the opposite of the shape of theconventional cyclic shift, as shown in the last cyclic shift of FIG. 23.

The present invention determines whether the alias range of the secondadditional cyclic shift is an available range (i.e.,d_(u)−[P·N_(CS)+(G−1)·S]≧N_(ZC)−2d_(u)+N_(CS)), and determines whetherthe cyclic shift interval is available (i.e., X+N_(CS)≦2d_(u)). If it isdetermined that the cyclic shift interval is available (i.e.,X+N_(CS)≦2d_(u)),

FIG. 24 is a conceptual diagram illustrating an exemplary cyclic shiftin the case of Nzc=839, Ncs=40, and d_(u)=399 according to anotherembodiment of the present invention. In FIG. 24, each group includesthree cyclic shifts and no first additional cyclic shift (i.e., zerofirst additional cyclic shift). And, each group further includes asingle additional cyclic shift in which a relative position of the mainregion is opposite to that of the alias region. This second additionalcyclic shift does not occur when the fixed cyclic shift position is notused, as shown in FIG. 22. In this example, the number of totalrestricted cyclic shifts is “4”.

According to this embodiment, the present invention applies the numberof calculated groups, the number of restricted cyclic shifts per group,and the group length to Equations 41 and 42, and then establishes thecyclic shift-applying interval in consideration of the above-mentionedparameters.

According to another embodiment, a specific system with the fixed cyclicshift may determine the cyclic shift according to the following method.

Firstly, the total sequence range is divided by the cyclic shift value.

Next, the present invention searches for the range (±u or ±(m*Nzc−1)/u)in which the interference caused by the offset occurs in the first range(i.e., n=1). In this case, there are a plurality of ranges, each ofwhich has the interference.

For example, in the case of considering only the first interference, amaximum number of interference generation ranges may be set to “4”.

Next, if the first range is not overlapped with all of the interferenceranges caused by the offset, the first range is set to an availablerange, and the remaining ranges caused by the offset is set to arestricted range (also called a prohibition range).

The present invention goes to the next range (i.e., n=n+1), andrepeatedly searches for the range in which the interference is generatedby the offset.

While the present invention searches for the interference generationrange in the n-th range, if an observation range, several ranges causedby the offset, an pre-established available range, and pre-establishedprohibition ranges are not overlapped with each other, the presentinvention determines a current range to be an available range, anddetermines the above several ranges caused by the offset associated withthe current range to be prohibition ranges. If the above-mentionedprocess is repeated until reaching the last range, the present inventionmay determine the cyclic shift in the system including the fixed cyclicshift.

According to still another embodiment, the present invention may applythe aforementioned established cyclic shift—applying interval to onlythe high-mobility cell in a mobile communication system includingseveral cells.

In this case, the present invention may determine whether acorresponding cell has the high mobility by determining whether thefrequency offset associated with the cell is higher than a predeterminedlevel after acquiring the cell information. In this case, thepredetermined level is indicative of a frequency offset value, which canbe readily decided or modified by those skilled in the art.

Preferably, the present invention may control the Node-B or the UE todetermine whether the corresponding cell is the high-mobility cell.However, the UE has difficulty in estimating the frequency offset valueof each of other UEs contained in the cell. Therefore, it is morepreferable that the Node-B determines whether the corresponding cell isthe high-mobility cell in consideration of several UEs of the cell, andbroadcasts the resultant signal over the broadcast channel.

In the meantime, if it is determined that the corresponding cell is notindicative of the high-mobility cell, the present invention may includea process for allocating a sequence unallocated to the high-mobilitycell.

The following description shows that equations are modified into othersunder the same condition as that of the best mode, and a detaileddescription thereof will hereinafter be described.

In association with the best mode, the above-mentioned equations mayalso be denoted by the following expression.

If C_(v)=S·└v/P┘+(v mod P)·N_(CS), v=0, 1, . . . , (P·G+R−1) andE=└d_(u)/N_(CS)┘, F=└(N_(ZC)−2d_(u))/N_(CS)┘, in the alias-distancerange of Ncs≦d_(u)<(Nzc/3), the P and G values are denoted by P=E,S=2d_(u)+E·N_(CS), G=└F·N_(CS)/S┘.

If C_(v)=S·└v/P┘+(v mod P)·N_(CS), v=0, 1, K, (P·G+R−1) andE=└d_(u)/N_(CS)┘, F=└(N_(ZC)−2d_(u))/N_(CS)┘, in the alias-distancerange of (Nzc/3)≦d_(u)≦(Nzc−Ncs)/2, the P, S, G, and R values aredenoted by P=F, S=N_(ZC)−2d_(u)+F·N_(CS), G=└E·N_(CS)/S┘,R=min(└(d_(u)−G·S)/N_(CS)┘, F).

Next, the case of the restricted cyclic shift considering thepre-defined shift position (Case 2) will hereinafter be described usingother equations.

The u-th root ZC sequence having the region of zero correlation, i.e.,the v-th random access preamble, is defined byx_(u,V)(n)=x_(u)((n+C_(v)) mod N_(zc)). In this case, the C_(v) value isdefined by equation 45:

$\begin{matrix}{C_{v} = \left\{ \begin{matrix}{{v \cdot N_{CS}},} & {{v = 0},1,\ldots \mspace{14mu},\left( {\left\lfloor {N_{ZC}/N_{CS}} \right\rfloor - 1} \right),} & {{{for}\mspace{14mu} {low}\text{/}{middle}\mspace{14mu} {mobility}\mspace{14mu} {cell}}\mspace{11mu}} \\{{{S \cdot \left\lfloor {v/P} \right\rfloor} + {\left( {v\; {mod}\; P} \right) \cdot N_{CS}}},} & {{v = 0},1,\ldots \mspace{14mu},\left( {{P \cdot G} + R - 1} \right),} & {{for}\mspace{14mu} {high}\mspace{14mu} {mobility}\mspace{14mu} {cell}}\end{matrix} \right.} & \left\lbrack {{Equation}\mspace{14mu} 45} \right\rbrack\end{matrix}$

wherein, C_(P·G+R) ₁ _(+R) ₂ ⁻¹=X, if R₂=1, for high mobility cell.

In this case, the parameters of the high-mobility cell can be defined bythe following explanation.

In more detail, in the alias range of Ncs≦d_(u)<(Nzc/3), the P value isdenoted by P=└d_(u)/N_(CS)┘, the S value is denoted byS=(┌2d_(u)/N_(CS)┐+P)·N_(CS), and the G value is denoted byG=└N_(ZC)/S┘. A first additional cyclic shift R1 is denoted byR₁=max(└(N_(ZC)−2·d_(u)−G·S)/N_(CS)┘, 0), and a second additional cyclicshift R₂ is denoted by R₂=0.

In the alias range of (Nzc/3)≦d_(u)≦(Nzc−Ncs)/2, the P value is denotedby P=└(N_(ZC)−2·d_(u))/N_(CS)┘, the S value is denoted byS=(┌(N_(ZC)−2·d_(u))/N_(CS)┐+P)·_(N) _(CS), and the G value is denotedby G=└d_(u)/S┘. A first additional restricted cyclic shift is denoted byR₁=min(max(└(d_(u)−G·S)/N_(CS)┘, 0), P), a second additional restrictedcyclic shift R₂ is denoted by R₂=1 in the case of R₁=0 and “X−Ncs<2d_(u)”. In this case, the X value is denoted byX=┌(N_(ZC)−d_(u)+P·N_(CS)+(G−1)S)/N_(CS)┐·N_(CS).

In the restricted cyclic shift case of x_(u,V)(n)=x_(u)((n+C_(v)) modN_(zc)), the method for directly using the shift value of the v-threstricted cyclic shift has been disclosed. Differently from the method,another method for employing the Va value for Va-th restricted cyclicshift so that the restricted cyclic shift can be applied to the presentinvention. In more detail, the similar cyclic shift can be generatedusing the equation of x_(u,Va)(n)=x_(u)((n+round(v_(a)N_(cs))) modN_(zc)).

In the case of generating the cyclic shift using the above-mentionedmethod, the basic concept is equal to those of the above-mentionedmethods. However, different equations are applied to the above-mentionedmethods.

The case (Case 1) of the restricted cyclic shift having no considerationin the pre-defined shift position will be described using otherequations.

The index (v) for the cyclic shift is represented by the followingequation 46:

$\begin{matrix}{v = \left\{ \begin{matrix}{{{g \cdot S} + p},} & \begin{matrix}{{{{for}\mspace{14mu} v} = {{P \cdot g} + p}},} \\{{p = 0},1,\ldots \mspace{14mu},{P - 1},} \\{{g = 0},1,K,{G - 1}}\end{matrix} \\{{{G \cdot S} + r},} & \begin{matrix}{{{{for}\mspace{14mu} v} = {{P \cdot G} + r}},} \\{{r = 0},1,\ldots \mspace{14mu},{R - 1}}\end{matrix}\end{matrix} \right.} & \left\lbrack {{Equation}\mspace{14mu} 46} \right\rbrack\end{matrix}$

In the alias range of Ncs≦d_(u)<(Nzc/3), the P value is denoted byP=└d_(u)/N_(CS)┘, the S value is denoted by S=2d_(u)/N_(CS)+P, and the Gvalue is denoted by G=└N_(ZC)/(S·N_(CS))┘, and the additional restrictedcyclic shift R is denoted by R=max(└(N_(ZC)−2·d_(u))/N_(CS)−G·S┘, 0).

In the alias range of (Nzc/3)≦d_(u)≦(Nzc−Ncs)/2, the P value is denotedby P=└(N_(ZC)−2·d_(u))/N_(CS)┘, the S value is denoted byS=(N_(ZC)−2d_(u))/N_(CS)+P, the G value is denoted byG=d_(u)/(S·N_(CS))|, and the R value is denoted byR=min(max(└d_(u)/N_(CS)−G·S┘, 0), P).

If E=└d_(u)/N_(CS)┘, F=└(N_(ZC)−2d_(u))/N_(CS)┘, the above-mentionedexpression can be represented by other ways. In more detail, in thealias range of Ncs≦d_(u)<(Nzc/3), the P value is denoted by P=E, the Svalue is denoted by S=2d_(u)/N_(CS)+E, the G value is denoted byG=└F/S┘, and the R value is denoted byR=min(└N_(ZC)−2·d_(u))/N_(CS)−G·S┘, E).

In the alias range of (Nzc/3)≦d_(u)≦(Nzc−Ncs)/2, the P value is denotedby P=F, the S value is denoted by S=N_(ZC)/N_(CS)−2d_(u)/N_(CS)+P, the Gvalue is denoted by G=└E/S┘, and the R value is denoted byR=min(└d_(u)/N_(CS)−G·S┘, F).

Next, the restricted cyclic shift case (Case 2) considering thepre-defined shift position will be described using other equations.

The index (v) for the cyclic shift is represented by the followingequation 47:

$\begin{matrix}{v = \left\{ \begin{matrix}{{{g \cdot S} + p},} & \begin{matrix}\begin{matrix}{{{{for}\mspace{14mu} v} = {{P \cdot g} + p}},} \\{{p = 0},1,\ldots \mspace{14mu},{P - 1},}\end{matrix} \\{{g = 0},1,\ldots \mspace{14mu},{G - 1}}\end{matrix} \\{{{G \cdot S} + r_{1}},} & \begin{matrix}{{{{for}\mspace{14mu} v} = {{P \cdot G} + r_{1}}},} \\{{r_{1} = 0},1,\ldots \mspace{14mu},{R_{1} - 1}}\end{matrix} \\{{X + r_{2}},} & \begin{matrix}{{{{for}\mspace{14mu} v} = {{P \cdot G} + R_{1} + r_{2}}},} \\{{r_{2} = 0},1,\ldots \mspace{14mu},{R_{2} - 1}}\end{matrix}\end{matrix} \right.} & \left\lbrack {{Equation}\mspace{14mu} 47} \right\rbrack\end{matrix}$

In the alias range of Ncs≦d_(u)<(Nzc/3), the P value is denoted byP=└d_(u)/N_(CS)┘, the S value is denoted by S=(┌2d_(u)/N_(CS)┐+P), andthe G value is denoted by G=└N_(ZC)/(SN_(CS))┘, and the additionalrestricted cyclic shift R₁ is denoted byR₁=max(└(N_(ZC)−G·SN_(CS)−2·d_(u))/N_(CS)┘, 0).

In the alias range of (Nzc/3)≦d_(u)≦(Nzc−Ncs)/2, the P value is denotedby P=└=(N_(ZC)−2·d_(u))/N_(CS)┘, the S value is denoted byS=(┌(N_(ZC)−2·d_(u))/N_(CS)┐+P), the G value is denoted byG=└d_(u)/(SN_(CS))┘, and the R₁ value is denoted by.R=min(max(└(d_(u)−G·SN_(CS))/N_(CS)┘, 0), P).

If R₁=0 and X·N_(CS)+N_(CS)≦2d_(u), the R₂ value can be represented byR₂=1. In this case, the X value is denoted byX=┌(N_(ZC)−d_(u)+P·N_(CS)+(G−1)SN_(CS))/N_(CS)┐.

If E=└d_(u)/N_(CS)┘; s=d_(u) mod N_(CS); E′=┌2s/N_(CS)┐ andF=└(N_(ZC)−2d_(u))/N_(CS)┘; t=((N_(ZC)−2h_(u)) mod N_(CS); E=┌t/N_(CS)┐,in the alias range of Ncs≦d_(u)<(Nzc/3), the P value is denoted by P=E,the S value is denoted by S=2F+F′, the G value is denoted by G[E/S], andthe R2 value is denoted by R₂=min(E−G·S, F).

If R₁=0 and X·N_(CS)≦2d_(u)−N_(CS), the R₂ value can be represented byR₂=1. In this case, the X value is denoted by X=┌X′+F+(G−1)S┐,X′=(N_(ZC)−d_(z))/N_(CS).

As described above, according to the above-mentioned embodiments, in thecase of implementing the cyclic shifted sequence using the CAZACsequence, the present invention may define the cyclic shift set capableof removing the shift ambiguity caused by the frequency- ortiming-offset.

Also, in the case of accessing the unsynchronized channel, the frequencyoffset or the timing offset is not adjusted to this unsynchronizedchannel, so that the present invention can increase the strength of thischannel.

According to the influence range of the pulse-shaping filter, thepresent invention may define the cyclic shift set in which thefirst-order interference, the second-order interference, and the higherorder interference are considered.

It should be noted that most terminology disclosed in the presentinvention is defined in consideration of functions of the presentinvention, and can be differently determined according to intention ofthose skilled in the art or usual practices. Therefore, it is preferablethat the above-mentioned terminology be understood on the basis of allcontents disclosed in the present invention.

It will be apparent to those skilled in the art that variousmodifications and variations can be made in the present inventionwithout departing from the spirit or scope of the invention. Thus, it isintended that the present invention cover the modifications andvariations of this invention provided they come within the scope of theappended claims and their equivalents.

As apparent from the above description, the present invention can easilyestablish a cyclic shift (CS) interval at a specific location having nooverlapping by considering a channel response of a reception (Rx)sequence and an alias location of this reception (Rx) sequence, althougha reception (Rx) signal is shifted by a channel delay spreading or apropagation delay irrespective of categories of a domain generating asequence, so that it can greatly reduce the number of the detectionerrors and the false alarm rate.

And, if a sequence of the cyclic shift (CS) is allocated to a cellhaving a frequency offset of more than a predetermined level, thepresent invention can minimize the influence of a frequency offset on ahigh-mobility cell.

The present invention relates to a first method for allocating asequence to each cell in consideration of characteristics of the CAZACsequence, and a second method for establishing the cyclic shift to beapplied to the first method. Therefore, the present invention can beapplied to a wireless communication system (e.g., a UE and a Node-B).

Although the preferred embodiments of the present invention have beendisclosed for illustrative purposes, those skilled in the art willappreciate that various modifications, additions and substitutions arepossible, without departing from the scope and spirit of the inventionas disclosed in the accompanying claims.

What is claimed:
 1. A method for transmitting a random access preambleto a base station, the method comprising: generating the random accesspreamble from a Zadoff-Chu (ZC) sequence having a length N, wherein therandom access preamble is generated by considering a cyclic shift of theZC sequence; and transmitting the random access preamble to the basestation, wherein: the cyclic shift is given by using a variable Mcorresponding to a Doppler shift of one subcarrier spacing; andparameters associated with defining the cyclic shift are differentlydefined based on whether the variable M is less than ⅓ of the length N.2. The method according claim 1, wherein the parameters comprise anumber G of one or more groups defined from the ZC sequence, a length Sof each of the one or more groups, and a number P of one or moreapplicable cyclic shift opportunities for each of the one or moregroups.
 3. The method according to claim 2, wherein the number G, thelength S, and the number P are applicable when the variable M is lessthan N/3.
 4. The method according to claim 3, wherein a number of one ormore additional cyclic shift opportunities is defined when a remainingspace of the ZC sequence is greater than 2M+T, where ‘T’ is a length ofa cyclic shift unit.
 5. The method according to claim 3, wherein a totalnumber of applicable cyclic shift opportunities is more than amultiplication of the number G and the number P, if (N−G×S) is not lessthan (2M+T), where ‘T’ is a length of a cyclic shift unit.
 6. The methodaccording to claim 3, wherein: the number G of the one or more groups isdefined byG=└N/S┘; the number P of the one or more applicable cyclicshift opportunities is equal to or less than M/T, where ‘T’ is a lengthof a cyclic shift unit; and the length S is defined as S=2M+P×T.
 7. Themethod according to claim 2, wherein the number G is 1 when the variableM is not less than N/3.
 8. A method for receiving a random accesspreamble from a user equipment (UE), the method comprising: receivingthe random access preamble from the UE, wherein: the random accesspreamble is generated from a Zadoff-Chu (ZC) sequence having a length N,the random access preamble being generated by considering a cyclic shiftof the ZC sequence; the cyclic shift is given by using a variable Mcorresponding to a Doppler shift of one subcarrier spacing; andparameters associated with defining the cyclic shift are differentlydefined based on whether the variable M is less than ⅓ of the length N.9. The method according to claim 8, wherein the parameters comprise anumber G of one or more groups defined from the ZC sequence, a length Sof each of the one or more groups, and a number P of one or moreapplicable cyclic shift opportunities for each of the one or moregroups.
 10. The method according to claim 9, wherein the number G, thelength S, and the number P are applicable when the variable M is lessthan N/3.
 11. The method according to claim 10, wherein a number of oneor more additional cyclic shift opportunities is defined when aremaining space of the ZC sequence is greater than 2M+T, where ‘T’ is alength of a cyclic shift unit.
 12. The method according to claim 10,wherein a total number of applicable cyclic shift opportunities is morethan a multiplication of the number G and the number P, if (N−G×S) isnot less than (2M+T), where ‘T’ is a length of a cyclic shift unit. 13.The method according to claim 10, wherein: the number G of the one ormore groups is defined by G=└N/S┘; the number P of the one or moreapplicable cyclic shift opportunities is equal to or less than M/T,where ‘T’ is a length of a cyclic shift unit; and the length S isdefined as S=2M+P×T.
 14. The method according to claim 9, wherein thenumber G is 1 when the variable M is not less than N/3.
 15. A userequipment for transmitting a random access preamble to a base station,wherein the UE is configured to: generate the random access preamblefrom a Zadoff-Chu (ZC) sequence having a length N, wherein the randomaccess preamble is generated by considering a cyclic shift of the ZCsequence; and transmit the random access preamble to the base station,wherein: the cyclic shift is given by using a variable M correspondingto a Doppler shift of one subcarrier spacing; and parameters associatedwith defining the cyclic shift are differently defined based on whetherthe variable M is less than ⅓ of the length N.
 16. The user equipmentaccording to claim 15, wherein the parameters comprise a number G of oneor more groups defined from the ZC sequence, a length S of each of theone or more groups, and a number P of one or more applicable cyclicshift opportunities for each of the one or more groups.
 17. The userequipment according to claim 16, wherein the number G, the length S, andthe number P are applicable when the variable M is less than N/3. 18.The user equipment according to claim 17, wherein a number of one ormore additional cyclic shift opportunities is defined when a remainingspace of the ZC sequence is greater than 2M+T, where ‘T’ is a length ofa cyclic shift unit.
 19. The user equipment according to claim 17,wherein a total number of applicable cyclic shift opportunities is morethan a multiplication of the number G and the number P, if (N−G×S) isnot less than (2M+T), where ‘T’ is a length of a cyclic shift unit. 20.The user equipment according to claim 17, wherein: the number G of theone or more groups is defined by G=└N/S┘; the number P of the one ormore applicable cyclic shift opportunities is equal to or less than M/T,where ‘T’ is a length of a cyclic shift unit; and the length S isdefined as S=2M+P×T.
 21. The user equipment according to claim 16,wherein the number G is 1 when the variable M is not less than N/3. 22.A base station for receiving a random access preamble from a userequipment (UE), wherein the base station is configured to: receive therandom access preamble from the UE, wherein: the random access preambleis generated from a Zadoff-Chu (ZC) sequence having a length N, therandom access preamble being generated by considering a cyclic shift ofthe ZC sequence; the cyclic shift is given by using a variable Mcorresponding to a Doppler shift of one subcarrier spacing; andparameters associated with defining the cyclic shift are differentlydefined based on whether the variable M is less than ⅓ of the length N.23. The base station according to claim 22, wherein the parameterscomprise a number G of one or more groups defined from the ZC sequence,a length S of each of the one or more groups, and a number P of one ormore applicable cyclic shift opportunities for each of the one or moregroups.
 24. The base station according to claim 23, wherein the numberG, the length S, and the number P are applicable when the variable M isless than N/3.
 25. The base station according to claim 24, wherein anumber of one or more additional cyclic shift opportunities is definedwhen a remaining space of the ZC sequence is greater than 2M+T, where‘T’ is a length of a cyclic shift unit.
 26. The base station accordingto claim 24, wherein a total number of applicable cyclic shiftopportunities is more than a multiplication of the number G and thenumber P, if (N−G×S) is not less than (2M+T), where ‘T’ is a length of acyclic shift unit.
 27. The base station according to claim 24, wherein:the number G of the one or more groups is defined by G=└N/S┘; the numberP of the one or more applicable cyclic shift opportunities is equal toor less than M/T, where ‘T’ is a length of a cyclic shift unit; and thelength S is defined as S=2M+P×T.
 28. The base station according to claim23, wherein the number G is 1 when the variable M is not less than N/3.